Separation of Variables in 3D, waveguide.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Separation of Variables in 3D, waveguide"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An infinitely long rectangluar metal pipe (sides $a$ and $b$) is grounded, but one end, at $x=0$ is maintained at a specified potential $V_0(y,z)$. Find the potential inside the pipe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a 3D problem and thus:\n",
    "\n",
    "$$\\frac{\\partial^2V}{\\partial x^2}+\\frac{\\partial^2V}{\\partial y^2}+\\frac{\\partial^2V}{\\partial z^2}=0 \\label{eq:1}\\tag{1}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Boundary conditions (Dirichlet):\n",
    "\n",
    "1. $V=0$ when $y=0$\n",
    "2. $V=0$ when $y=a$\n",
    "3. $V=0$ when $z=0$\n",
    "4. $V=0$ when $z=b$\n",
    "5. $V\\rightarrow0$ as $x\\rightarrow \\infty$\n",
    "3. $V=V_0(y,z)$ when $x=0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Separation of variables: as products\n",
    "\n",
    "$$V(x,y,z)=X(x)Y(y)Z(z)\\tag{2}$$\n",
    "\n",
    "$$\\frac 1 X \\frac{d^2X}{dx^2}+\\frac 1 Y \\frac{d^2Y}{dy^2}+\\frac 1 Z \\frac{d^2Z}{dz^2}=0\\tag{3}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Three constants: $C_1$:positive, $C_2$:negative, $C_3$:negative\n",
    "\n",
    "$$ C_2 = -k^2,\n",
    "C_3 = -l^2,\n",
    "C_1 = k^2 + l^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This turns a PDE in three ODEs which we can solve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.interactive import printing # use latex for printing\n",
    "printing.init_printing(use_latex=True)\n",
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols # import necessary methods\n",
    "from sympy.abc import x,y,z # import variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$- \\left(k^{2} + l^{2}\\right) X{\\left (x \\right )} + \\frac{d^{2}}{d x^{2}} X{\\left (x \\right )} = 0$$"
      ],
      "text/plain": [
       "                     2          \n",
       "  ⎛ 2    2⎞         d           \n",
       "- ⎝k  + l ⎠⋅X(x) + ───(X(x)) = 0\n",
       "                     2          \n",
       "                   dx           "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = Function('X',real=True)\n",
    "k, l = symbols('k l',positive=True)\n",
    "f1_ode = Eq(Derivative(X(x), x, 2) - (k**2+l**2)*X(x))\n",
    "f1_ode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$X{\\left (x \\right )} = C_{1} e^{- x \\sqrt{k^{2} + l^{2}}} + C_{2} e^{x \\sqrt{k^{2} + l^{2}}}$$"
      ],
      "text/plain": [
       "                 _________            _________\n",
       "                ╱  2    2            ╱  2    2 \n",
       "           -x⋅╲╱  k  + l         x⋅╲╱  k  + l  \n",
       "X(x) = C₁⋅ℯ                + C₂⋅ℯ              "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol1 = dsolve(f1_ode, X(x))\n",
    "sol1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$k^{2} Y{\\left (y \\right )} + \\frac{d^{2}}{d y^{2}} Y{\\left (y \\right )} = 0$$"
      ],
      "text/plain": [
       "            2          \n",
       " 2         d           \n",
       "k ⋅Y(y) + ───(Y(y)) = 0\n",
       "            2          \n",
       "          dy           "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = Function('Y',real=True)\n",
    "f2_ode = Eq(Derivative(Y(y), y, 2) + k**2*Y(y))\n",
    "f2_ode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$Y{\\left (y \\right )} = C_{1} \\sin{\\left (k y \\right )} + C_{2} \\cos{\\left (k y \\right )}$$"
      ],
      "text/plain": [
       "Y(y) = C₁⋅sin(k⋅y) + C₂⋅cos(k⋅y)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol2 = dsolve(f2_ode, Y(y))\n",
    "sol2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$l^{2} Z{\\left (z \\right )} + \\frac{d^{2}}{d z^{2}} Z{\\left (z \\right )} = 0$$"
      ],
      "text/plain": [
       "            2          \n",
       " 2         d           \n",
       "l ⋅Z(z) + ───(Z(z)) = 0\n",
       "            2          \n",
       "          dz           "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = Function('Z',real=True)\n",
    "f3_ode = Eq(Derivative(Z(z), z, 2) + l**2*Z(z))\n",
    "f3_ode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$Z{\\left (z \\right )} = C_{1} \\sin{\\left (l z \\right )} + C_{2} \\cos{\\left (l z \\right )}$$"
      ],
      "text/plain": [
       "Z(z) = C₁⋅sin(l⋅z) + C₂⋅cos(l⋅z)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol3 = dsolve(f3_ode, Z(z))\n",
    "sol3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From boundary conditions (except (6)) we get:\n",
    "\n",
    "$$V(x,y,z)=C\\textrm{e}^{-\\pi \\sqrt{(n/a)^2+(m/b)^2}x} \\sin{(n\\pi y/a)} \\sin{(m\\pi z/b)}$$\n",
    "\n",
    "with\n",
    "\n",
    "$$ k = \\frac{n\\pi}{a},\\ l=\\frac{m\\pi}{b}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which we can use to define a double sum for all possible $V_0(y,z)$\n",
    "\n",
    "$$ V(x,y,z)= \\sum_{n=1}^{\\infty}\\sum_{m=1}^{\\infty} C_{n,m}\\textrm{e}^{-\\pi \\sqrt{(n/a)^2+(m/b)^2}x} \\sin{(n\\pi y/a)} \\sin{(m\\pi z/b)} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and get the coefficients $C_{n,m}$ from BC (6)\n",
    "\n",
    "$$ V(0,y,z)= \\sum_{n=1}^{\\infty}\\sum_{m=1}^{\\infty} C_{n,m} \\underbrace{\\textrm{e}^{-\\pi \\sqrt{(n/a)^2+(m/b)^2}x}}_{=1 \\textrm{ for }x=0} \\sin{(n\\pi y/a)} \\sin{(m\\pi z/b)} = V_0(y,z)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "using the same approach again and multiplying with:\n",
    "\n",
    "$$ \\sin{(n'\\pi y/a)} \\sin{(m'\\pi z/b)}$$\n",
    "\n",
    "and integrating from 0 to $a$ and 0 to $b$:\n",
    "\n",
    "$$ \\sum_{n=1}^{\\infty}\\sum_{m=1}^{\\infty} C_{n,m} \\int_0^a \\sin{(n\\pi y/a)} \\sin{(n'\\pi y/b)}\\,dy \\int_0^b \\sin{(m\\pi z/a)} \\sin{(m'\\pi z/b)}\\,dz  = \\int_0^a \\int_0^b V_0 \\sin{(n'\\pi y/a)} \\sin{(m'\\pi z/b)}\\,dydz$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "solving the integrals on the left side:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\begin{cases} 0 & \\text{for}\\: \\left(k \\neq l \\wedge m \\neq n\\right) \\vee k \\neq l \\vee m \\neq n \\\\\\frac{a b}{4} & \\text{otherwise} \\end{cases}$$"
      ],
      "text/plain": [
       "⎧ 0   for (k ≠ l ∧ m ≠ n) ∨ k ≠ l ∨ m ≠ n\n",
       "⎪                                        \n",
       "⎨a⋅b                                     \n",
       "⎪───               otherwise             \n",
       "⎩ 4                                      "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import integrate, pi\n",
    "n, m, k, l = symbols('n m k l', positive = True, integer=True)\n",
    "a, b = symbols('a b', constant = True)\n",
    "integrate(integrate(sin(n*pi*y/a)*sin(m*pi*y/a)*sin(k*pi*z/b)*sin(l*pi*z/b), (y, 0, a)), (z, 0, b)) # var y, from 0 to a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we get for $C_{n,m}$:\n",
    "\n",
    "$$ C_{n,m} = \\frac{4}{ab} \\int_0^a \\int_0^b V_0(y,z) \\sin{(n\\pi y/a)} \\sin{(m\\pi z/b)}\\,dydz$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example: $V_0(y,z)$ is constant:\n",
    "\n",
    "$$ C_{n,m} = \\frac{4V_0}{ab} \\int_0^a \\int_0^b \\sin{(n\\pi y/a)} \\sin{(m\\pi z/b)}\\,dydz = \\begin{cases}\n",
    "    0, & \\text{if $n$ or $m$ is even}.\\\\\n",
    "    \\frac{16V_0}{nm\\pi^2}, & \\text{if $n$ is odd}.\n",
    "\\end{cases}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and thus:\n",
    "\n",
    "$$ V(x,y,z)= \\frac{16 V_0}{\\pi^2} \\sum_{n,m=1,3,5,\\ldots}^{\\infty} \\frac{1}{nm}\\textrm{e}^{-\\pi \\sqrt{(n/a)^2+(m/b)^2}x} \\sin{(n\\pi y/a)} \\sin{(m\\pi z/b)} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
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       "\n",
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       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"500\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "fig = plt.figure(figsize=(5.,5.))\n",
    "ax = fig.gca(projection='3d')\n",
    "\n",
    "n=1\n",
    "m=1\n",
    "a=1\n",
    "b=1\n",
    "V0 = 1\n",
    "x = np.arange(0,1.01,0.01)  # range for x\n",
    "y = np.arange(0,a+0.01,0.01)  # range for y\n",
    "#z = np.arange(0,b+0.01,0.01)\n",
    "X,Y = np.meshgrid(x,y)  # generate 2D mesh from x and y\n",
    "Z=.1\n",
    "V=(16*V0/np.pi**2)*(1/(n*m)*np.exp(-np.pi*np.sqrt((n/a)**2+(m/b)**2)*x)*np.sin(n*np.pi*Y/a)*np.sin(m*np.pi*Z/b))  # define V(x,y) on the mesh X,Y\n",
    "\n",
    "# Plot a crossection\n",
    "cset = ax.contour3D(X, Y, V, zdir='z', offset=.1, cmap='Blues',levels=64) # lineplot on the xz plane\n",
    "ann = ax.text(.7,.8,1, \"n={}\".format(n), color='k',fontsize=24) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}