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Special functions in phase space: Mathieu functions. (English) Zbl 0960.81038

Summary: The authors introduce functions which are solutions to a coherent-state representation of the Schrödinger equation for the pendulum potential. These functions are interpolation functions between the coordinate and momentum solutions for the quantum pendulum. They also introduce their classical analogues which are stationary solutions to the classical Liouville equation.

MSC:

81R30 Coherent states
33E10 Lamé, Mathieu, and spheroidal wave functions
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
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