The three-dimensional quartic oscillator

Abstract

Accurate eigenvalues and selected eigenvectors are presented for the three-dimensional isotropic quartic oscillator in the representation of the three-dimensional isotropic harmonic oscillator. They were determined by means of the linear variation method, and matrices of large order were diagonalized by using efficient procedures. This work rectifies an error in the calculations of Lu and Nigam (1969), which results in only half of their energy levels being the true solutions of the quartic oscillator problem.