Non spherical solutions of a spherical potential well?

In summary, the solutions of a spherical potential well can have no spherical symmetry, meaning that the probability distribution for finding a particle described by an eigenstate of the Hamiltonian may not depend on the angular coordinate. However, for solutions with angular momentum greater than 0, there will be an angular distribution due to a defined z axis.
  • #1
nista
11
0
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
 
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  • #2
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.
 

FAQ: Non spherical solutions of a spherical potential well?

What is a non-spherical solution of a spherical potential well?

A non-spherical solution of a spherical potential well refers to the theoretical model of a particle in a potential well that is not symmetrical in all directions. In other words, the potential well is not perfectly spherical and can vary in shape and depth.

How does a non-spherical potential well affect the behavior of particles?

A non-spherical potential well can lead to more complex and diverse behaviors of particles compared to a spherical potential well. For example, particles may exhibit oscillatory or chaotic motion, depending on the specific shape and depth of the well.

What factors contribute to the non-spherical shape of a potential well?

The shape of a potential well can be affected by various factors such as the presence of other particles, external forces, and the distribution of mass within the well. In some cases, the geometry of the system itself can also lead to a non-spherical potential well.

How do scientists study non-spherical solutions of a spherical potential well?

Scientists use mathematical models and simulations to study the behavior of particles in non-spherical potential wells. They also conduct experiments using charged particles in electric fields or trapped atoms in laser beams to observe and analyze the effects of non-spherical potential wells.

What applications do non-spherical potential wells have in physics?

Non-spherical potential wells have various applications in physics, including understanding the behavior of particles in complex systems, studying the stability of celestial bodies, and developing new technologies such as particle accelerators and quantum computers.

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