# Three-Dimensional Isotropic Harmonic Oscillator

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The isotropic three-dimensional harmonic oscillator is described by the Schrödinger equation , in units such that . The wavefunction is separable in Cartesian coordinates, giving a product of three one-dimensional oscillators with total energies . More interesting is the solution separable in spherical polar coordinates: , with the radial function . Here, is an associated Laguerre polynomial, , a spherical harmonic and , a normalization constant. The energy levels are then given by , being -fold degenerate. For a given angular momentum quantum number , the possible values of are . The conventional code is used to label angular momentum states, with representing .

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

Open content licensed under CC BY-NC-SA

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Reference: Wikipedia article Quantum Harmonic Oscillator

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