Non spherical solutions of a spherical potential well?

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SUMMARY

The discussion centers on the understanding of non-spherical solutions in a spherical potential well, specifically regarding the implications of angular momentum on probability distributions. Roberto clarifies that while a spherically symmetric potential allows for equal likelihood of all m values for each L, the introduction of a defined axis results in an angular distribution, thus breaking spherical symmetry. This highlights the relationship between angular momentum and the spatial probability distribution of quantum states.

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nista
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Hi all
just a question about the understanding of the solutions of a spherical potential well.
What is the physical sense of solutions which have no spherical symmetry?
I just would think that the probability of finding a particle
whose state is described by one of the eigenstate of the Hamiltonian should not depend on the angular coordinate as the
problem as spherical symmetry. However for solutions with angular momentum larger than 0 this not the case. Why?
Thanks in advance for your comments

Roberto
 
Physics news on Phys.org
If there is no preferred direction, so all the m values for each L are equally likely, the full probability distribution will be spherically symmetric. If there is a defined z axis for which different m values have different amplitudes, there will be an angular distribution.
 

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