Hermite polynomials with many variables and many indices play a crucial role within the framework of phase-space formulation of classical or quantum mechanics. A generalized operational formalism useful to handle these polynomials is discussed and also a new set of creation-annihilation operators associated to the phase-space harmonic oscillator orthogonal functions is introduced. The Fourier transform of these orthogonal functions is studied by discussing the analogies with the ordinary case. Finally, the integral representation of the generalized Hermite polynomials and a simple technique to deal with the generalized heat equation are discussed. © 1995 American Institute of Physics.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
Dattoli, G., & Torre, A. (1995). Phase-space formalism: Generalized Hermite polynomials, orthogonal functions and creation-annihilation operators. Journal of Mathematical Physics, 36(4), 1636 - 1644. https://doi.org/10.1063/1.531075