Calculation of the wave functions of a quantum asymmetric top using the noncommutative integration method

TL;DR

This paper applies the noncommutative integration method to solve the Schrödinger equation for a quantum asymmetric top, deriving solutions via Lame polynomials and analyzing the spectrum through group invariance conditions.

Contribution

It introduces a novel application of the noncommutative integration method to quantum asymmetric tops, linking solutions to Lame equations and group representation theory.

Findings

Derived complete solutions using Lame polynomials

Connected solutions to the geometry of coadjoint orbits

Obtained the spectrum from invariance conditions

Abstract

In this work, using the noncommutative integration method of linear differential equations, we obtain a complete set of solutions to the Schrodinger equation for a quantum asymmetric top in Euler angles. It is shown that the noncommutative reduction of the Schrodinger equation leads to the Lame equation. The resulting set of solutions is determined by the Lame polynomials in a complex parameter, which is related to the geometry of the orbits of the coadjoint representation of the rotation group. The spectrum of an asymmetric top is obtained from the condition that the solutions are invariant with respect to a special irreducible $\lambda$-representation of the rotation group.