Torres-Vega, Go.; Morales-Guzmán, J. D.; Zúñiga-Segundo, A. Special functions in phase space: Mathieu functions. (English) Zbl 0960.81038 J. Phys. A, Math. Gen. 31, No. 31, 6725-6739 (1998). 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. Cited in 1 Document 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 Keywords:phase-space functions; Mathieu functions; classical limit; coherent-state representation; Schrödinger equation; pendulum potential; quantum pendulum PDFBibTeX XMLCite \textit{Go. Torres-Vega} et al., J. Phys. A, Math. Gen. 31, No. 31, 6725--6739 (1998; Zbl 0960.81038) Full Text: DOI Digital Library of Mathematical Functions: 8th item ‣ §28.33(iii) Stability and Initial-Value Problems ‣ §28.33 Physical Applications ‣ Applications ‣ Chapter 28 Mathieu Functions and Hill’s Equation