Eigenvalues for a Pure Quartic Oscillator

TL;DR

This paper computes eigenvalues for a pure quartic oscillator using a canonical operator approach, achieving high accuracy and confirming previous results with a straightforward secular equation method.

Contribution

It introduces a canonical operator formulation for the quartic oscillator and demonstrates its effectiveness in accurately computing eigenvalues.

Findings

Eigenvalues computed agree with literature to at least 4 significant figures

A 10x10 secular equation suffices for accurate eigenvalue estimation

Method confirms the validity of the canonical operator approach for nonlinear oscillators

Abstract

The eigenvalues of a pure quartic oscillator are computed, applying a canonical operator formulation, generalized from the harmonic oscillator. Solving a 10x10 secular equation produces eigenvalues in agreement, to at least 4 significant figures, with accurate computations given in the literature.