Spherically symmetric potential

Coulomb potential

Consider a particle of charge and mass bound to a stationary charge at the origin. The potential experienced by the particle, given by Coulomb's law, is spherically symmetric with

giving the radial equation

which has bound states

where is a spherical harmonic, is an Associated Laguerre polynomial, and

which in the case of hydrogen is the Bohr radius. The allowable energies are

which are each -degenerate.

Quantum numbers

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