Abstract
In the quantization of a rotating rigid body, a top, one is concerned with the Hamiltonian operator Lα = α20L2x + α21L2y + α22L2z, where α0 ⩽ α1 ⩽ α2. An explicit formula is known for the eigenvalues of Lα in the case of the spherical top (α1 = α2 = α3) and symmetrical top (α1 = α2 ≠ α3) (Landau and Lifshitz 1981 Quantum Mechanics: Non-Relativistic Theory 3rd edn (Portsmouth, NH: Butterworth-Heinemann)). 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 Lα = α20L2x + α21L2y + α22L2z for any α0 < α1 < α2.
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