Kowalevski top in quantum mechanics

• Published in: Annals of physics Vol. 336; pp. 130 - 166
• Main Author: Matsuyama, A.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.09.2013; Elsevier BV
• Subjects: Action variable; BIFURCATION; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENSTATES; Formulations; HAMILTONIANS; Integers; Invariants; Kowalevski top; Maslov index; Mathematical analysis; QUANTIZATION; QUANTUM MECHANICS; QUANTUM NUMBERS; Quantum physics; Quantum spectrum; SEMICLASSICAL APPROXIMATION; Semiclassical quantization; SPECTRA; SYMMETRY; Kowalevski top; Semiclassical quantization; Maslov index; Quantum spectrum; Action variable
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2013.05.019

The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra. •Quantum spectra of the Kowalevski top are calculated.•Semiclassical quantization is carried out by the EBK formulation.•Quantum states are labeled by the semiclassical integer quantum numbers.•Multiplicity of the classical torus makes the spectra nearly degenerate.•Symmetries, quantum numbers and near-degenerate spectra are closely related.