# Particle in an Infinite Spherical Well

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A particle of mass in an infinite spherical potential well of radius is described by the Schrödinger equation . The wavefunction is separable in spherical polar coordinates, such that , where is a spherical harmonic, a spherical Bessel function, and is a normalization constant. The boundary condition that at is fulfilled when is the zero of the spherical Bessel function . The quantized energy levels are then given by and are -fold degenerate with . The conventional code is used to label angular momentum states, with representing . Unlike atomic orbitals, the -values are not limited by ; thus one will encounter states designated , etc.

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Contributed by: S. M. Blinder (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshots 1–3: the three lowest energy states

Snapshot 4: energy-level diagram

## Permanent Citation