Boundary Conditions
As with all quantum mechanics problems, if the boundary conditions are changed so does the wave function. If a particle is confined to the motion of an entire ring ranging from 0 to, the particle is subject only to a periodic boundary condition (see particle in a ring). If a particle is confined to the motion of to, the issue of even and odd parity becomes important.
The wave equation for such a potential is given as:
where and are for odd and even m respectively.
Similarly, if the semicircular potential well is a finite well, the solution will resemble that of the finite potential well where the angular operators and replace the linear operators x and p.
Read more about this topic: Semicircular Potential Well
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