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arXiv · 0706.4127

Semiclassical Density of States for the Quantum Asymmetric Top

Alfonso F. Agnew·Alain Bourget
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Abstract

In the quantization of a rotating rigid body, a {\it top,} one is concerned with the Hamiltonian operator $L_α=α_0^2 L_x^2 + α_1^2 L_y^2 + α_2^2 L_z^2,$ where $α_0 < α_1 <α_2.$ An explicit formula is known for the eigenvalues of $L_α$ in the case of the spherical top ($α_1 = α_2 = α_3$) and symmetrical top ($α_1 = α_2 \neq α_3$) \cite{LL}. However, for the asymmetrical top, no such explicit expression exists, and the study of the spectrum is much more complex. In this paper, we compute the semiclassical density of states for the eigenvalues of the family of operators $L_α=α_0^2 L_x^2 + α_1^2 L_y^2 + α_2^2 L_z^2$ for any $α_0 < α_1 <α_2$.

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Alfonso F. Agnew, Alain Bourget. 2007-06-28. Semiclassical Density of States for the Quantum Asymmetric Top. https://arxiv.org/abs/0706.4127

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