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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:
81R30Coherent states; squeezed states (quantum theory)
33E10Lamé, Mathieu, and spheroidal wave functions
81S30Phase space methods in quantum mechanics