Quartic Oscillator as a Basis for Energy Level Calculations of Some Anharmonic Oscillators

Abstract

A variational treatment facilitating accurate energy level calculations for the mixed harmonic—quartic oscillator within the frameworks of both the harmonic oscillator and the quartic oscillator representations is formulated. The usefulness of the quartic oscillator as a basis for such calculations is examined in detail. It is shown that the quartic oscillator representation yields significantly better energies than the conventional harmonic oscillator representation even for moderate quartic anharmonicities. The first 10 energy levels, expectation values of x2, x4, and some transition moments are presented over the range of anharmonicities from the pure harmonic oscillator to the pure quartic oscillator.