The rotating harmonic oscillator revisited

TL;DR

This paper revisits the quantum rotating harmonic oscillator, deriving eigenvalues and eigenfunctions analytically through a Frobenius method and recurrence relations, enhancing understanding of its spectral properties.

Contribution

It provides a new analytical approach to determine the spectrum of the quantum rotating harmonic oscillator using Frobenius method and recurrence relations.

Findings

Exact eigenvalues and eigenfunctions obtained for specific cases.

Organization of eigenvalues offers insights into the entire spectrum.

Analytical truncation method improves spectral analysis.

Abstract

We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation of the series yields some particular eigenvalues and eigenfunctions in exact analytical form. The former can be organized in such a way that one obtains suitable information about the whole spectrum of the model.