- #1

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In other words is it possible for psi and psi* to change phases during orbital state transitions?

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- Thread starter DmplnJeff
- Start date

If energy is being conserved then the phase space shouldn't change.The wave function is complex. I was taught that its square (probability) was actually psi times it's conjugate. Does this relationship always hold or was this only for bound and free particles? The magnitude squared of the number is always equal to the number times its conjugate. This is a universal property of complex numbers.f

- #1

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In other words is it possible for psi and psi* to change phases during orbital state transitions?

- #2

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[tex]Z = x + iy[/tex]

[tex]Z^* = x - iy[/tex]

[tex]ZZ^* = (x + iy)(x - iy) = x^2 -i^2y^2 = x^2 + y^2[/tex]

So in polar coordinates, where [tex]r = \sqrt{x^2 + y^2}[/tex], the number times its conjugate will always be [tex]r^2[/tex].

- #3

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What happens when these waves overlap? There are two possibilities (as I think):

1) The electrons entangle and there will be only one two-electron instead of two electrons,

2) They overlap without any interaction.

- #4

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The wave function is complex. I was taught that its square (probability) was actually psi times it's conjugate. Does this relationship always hold or was this only for bound and free particles?

Its square modulus is always psi*psi. The easiness with which we ascribe a probabilistic interpretation to this modulus is dictated on whether psi is an element of a Hilbert space, thus is finite norm, or its modulus is finite, so it can be rescaled to unity.

DmplnJeff said:In other words is it possible for psi and psi* to change phases during orbital state transitions?

The orbital state transitions are determined by an external intervention in an initially closed atomic system. The dynamics is then described by the Schroedinger equation whose solution cannot be really found analytically. The phase of the wavefunction during transition cannot be therefore determined exactly, but only proved to different than the one pertaining to a wavefunction of an unperturbed atomic system.

- #5

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Basically I'm trying to understand what solutions are available for Schroedinger's equation during the transition (if Schroedinger's equation applies?). So far what I've read amounts to a transition being some sort of miracle. It just happens.

Possible solutions depend on whether psi^2 is one number squared or two numbers.

- #6

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That theorem applies to non-dissipative spaces. Yet during the absorption (or emission) of a photon energy is not being conserved (locally). Why doesn't that make a difference?

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