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Coherent states for the quantum complete rigid rotor. (English) Zbl 1388.81231

Summary: Motivated by the possibility to describe orientations of quantum triaxial rigid rotors, such as molecules, with respect to both internal (body-fixed) and external (laboratory) frames, we go through the theory of coherent states and design the appropriate family of coherent states on \(\mathrm{T}^\ast \mathrm{SO}(3)\), the classical phase space of the freely rotating rigid body (the Euler top). We pay particular attention to the resolution of identity property in order to establish the explicit relation between the parameters of the coherent states and classical phase-space variables, actions and angles.

MSC:

81R30 Coherent states
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
81S10 Geometry and quantization, symplectic methods
53D50 Geometric quantization
81V55 Molecular physics
70E05 Motion of the gyroscope

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