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

• URL: http://arxiv.org/abs/2211.14812v2
• Date: Fri, 23 Dec 2022 09:50:19 GMT
• Title: Calculation of the wave functions of a quantum asymmetric top using the noncommutative integration method
• Authors: A. I. Breev and D. M. Gitman
• Abstract summary: We obtain a complete set of solutions to the Schrodinger equation for a quantum asymmetric top in Euler angles. The spectrum of an asymmetric top is obtained from the condition that the solutions are in with respect to a special irreducible $lambda$-representation of the rotation group.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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