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Spinnor

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Thanks!

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- #1

Spinnor

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Thanks!

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Your suggestion doesn't appear to be normalizable if you allow ##z\in(-\infty,\infty)##. Consider ##\int |\Psi|^2 \mathrm{d}zr\mathrm{d}r\mathrm{d}\theta##. You are forced to do the integral ##\int\limits_{-\infty}^{\infty}1\mathrm{d}z##.

EDIT: I suppose the answer to your exact question is that, yes, it could be a wavefunction with an appropriate restriction on the domain in the z-direction.

EDIT: I suppose the answer to your exact question is that, yes, it could be a wavefunction with an appropriate restriction on the domain in the z-direction.

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- #3

blue_leaf77

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Judging from the expression of the wavefunction, there can be two possibilities about the condition of the potential along the z-direction:1) The potential is constant along this direction, for which reason ##p## is continuous or 2) there is an infinite square well confining the space along z direction, in this case ##p## must be discrete.

Thanks!

Either way, the function you have there is bounded at infinities and therefore it can act as a basis function, despite being not normalizable for the case of continuous ##p##, for a physically realizable state.

EDIT: The only possible potential form in the z direction in this case is a constant potential. Therefore ##p## must be continuous.

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- #4

Spinnor

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Thanks!

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blue_leaf77

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Spin? That was not mentioned in your original post.

- #6

Spinnor

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Spin? That was not mentioned in your original post.

Yes, but but my function depends on angular coordinates (there is angular momentum?). My function only returns to itself after a 4π rotation and I'm not sure that is acceptable.

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- #7

blue_leaf77

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Rotation operator due to spin angular momentum can only rotate spin state, it does not act on spatial wavefunction.My function only returns to itself after a 4π rotation and I'm not sure that is acceptable.

- #8

Spinnor

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The second more worrisome problem is the fact that the function only returns to itself after two complete rotations,

Ψ=f(r)exp[-i(Et-pz+Φ/2)] = Ψ=f(r)exp[-i(Et-pz+[Φ+4π]/2)]

What trouble do we get in if Ψ(r,z,Φ) ≠ Ψ(r,z,Φ+2π) but Ψ(r,z,Φ) = Ψ(r,z,Φ+4π)?

Thanks Blue_leaf for your help!

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