Ladder Operators for the Spherical 3D Harmonic Oscillator

Abstract

The Schrödinger equation for an isotropic three-dimensional harmonic oscillator is solved using ladder operators. The starting point is the shape invariance condition, obtained from supersymmetric quantum mechanics. Generalized ladder operators can be constructed for the three spherical spatial coordinates. Special emphasis is given to the adaptation made to each of these coordinates. The approach used is general and is indicated as an alternative method to solve the Schrödinger equation.

Keywords

• Ladder operators
• Harmonic oscillator
• Shape invariance
• Supersymmetric quantum mechanics