Particle in an Infinite Circular Well

m

1

k

1

plot

density

3D

contour

This Demonstration solves the quantum-mechanical problem of a particle confined to a disk, which can be called an infinite 2D circular well. The probability densities for several energy eigenstates are plotted. The azimuthal quantum number

m

, equal to the number of angular nodes, determines the angular momentum

mℏ

. The radially excited state energies depend on the zeros of the Bessel function

J

m

(kr)

.