calculate the energy eigenvalues of a particle confined to a ring of radius a?

Answer 1

Treat this just like a particle in a box (infinite square well) except that the quantization condition is a bit different.

Instead of insisting that the wave function is zero at the edges, you just insist that the wave function (as a function of angle now) be single valued. So it has to have a period of 2pi/n where n is a positive integer.

Do everything else the same and you get almost the same answer.

Answer 2

n^2 a