The Quantum Mechanical Spherical Harmonic Oscillator

The quantum mechanical motion of a particle in a central field - here referred to as the central field problem - is prominently featured in the core physical chemistry curriculum. While analysis of the general problem is appropriately effected using spherical polar coordinates, many students find daunting the use of spherical polar coordinates in this context. With this in mind, it may be helpful to introduce analysis of the central field problem through a case which can be readily solved using Cartesian coordinates, specifically the spherical harmonic oscillator. A presentation is given of the spherical harmonic oscillator at the level of the core physical chemistry courses.