We discuss the mathematical properties of phase space harmonic-oscillator orthogonal functions. We introduce the relevant creation-annihilation operators and point out the existence of generalized uncertainty, relations of the Heisenberg type. We define coherent phase space states and show that they are generalized minimum uncertainty states. We apply the methods developed to the analysis of classical and quantum harmonic oscillators and, within such a context propose an operator formalism that permits one to exploit Heisenberg-like equations in both classical and quantum problems. © 1995 Società Italiana di Fisica.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
Dattoli, G., & Torre, A. (1995). Phase space formalism: The generalized harmonic-oscillator functions. Nuovo Cimento della Societa Italiana di Fisica B, 110(10), 1197 - 1212. https://doi.org/10.1007/BF02724610