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other uses of wavefunction(ÊΨ=EΨ; ...)
Wavefunction.txt
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| [t] As an introduction to the wavefunction we may have a quick reconciliation on the wave-model. So the first part that was introduced was the wavelength, it basically meant, that there was an uncertainty of the position of the quantum object. But while this meant that we just thought to know that the particle was somewhere "in there". However now things have changed, into both directions. \ | |||
| On one side we now can give clearer information about the position in the space determined by the wavelength. On the other side we have clarified that there is a small but existing probability of the quantum object being outside of that space. \ | |||
| The wavefunction is usually written as \Psi(x, y, z, t) or just as a function of a selected amount of those variables. It is the core of quantum theory and it is the function wich is the solution to the Schroedinger-equation, which is of course a differential equation so it has a function as a solution. One can express it's meaning very simply by stating, that: [\] | |||
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\Psi != Ψ
which is of course a differential equation so it has a function as a solution
neccesary?
IntegratedQuantum
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| As far as I am concerned there is just no way to know this. The problem is the only thing the equations of quantum physics (mainly the Schroedinger-equation) do not tell us exactly how the universe is. But what they tell us, is that it is unclear. There may be some equations one day that tell us how exactly the universe is. But in this moment we do not know. \ | ||
| And maybe the position is just not determined yet, so in the instance of time you measure the position of a particle it gets set up and before that the position is not only unknown to you but also not there. But this is just one interpretation of the equations (Hyperlink: Interpretations). \ | ||
| One small excurse would be the mentioning of the most famous use of the wavefunction or to be more correct the square of the absolute value of it (|Ψ|^2 ), the use are the Atomic Orbitals. Every part in the space around the nucleus that has under the given potential a probability of over 90% for finding the electron is part of the orbital. There we can see the changes from just the sheer wavelength to the wavefunction. \ | ||
| If we would just have the wavelength it would be enough to say, that the electron is in a specific orbital, but with the wavefunction that just is not the whole question. [\] |
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maybe reference to Tunnel Effect?
| On one side we now can give clearer information about the position of the quantum object in the same sphere. On the other side we have clarified that there is a small but existing probability of the quantum object being outside of that sphere. \ | ||
| The wavefunction is usually written as Ψ(x, y, z, t) or just as a function of a selected amount of those variables. It is the core of quantum theory and it is the function wich is the solution to the Schroedinger-equation, which is of course a differential equation so it has a function as a solution. One can express it's meaning very simply by stating, that: [\] | ||
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| [f] | Ψ(x, y, z, t)|^2 = p(x, y, z, t) [\] |
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more generally for all observables:
∫Ψ*operatorΨ dτ
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