Study on a Phase Space Representation of Quantum Theory

Abstract

A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current formulation of quantum mechanics which is based on the use of Hilbert space and linear operators theory. Phase space representation of quantum states and wave functions in phase space are introduced using properties of a set of functions called harmonic Gaussian functions. Then, new operators called dispersion operators are defined and identified as the operators which admit as eigenstates the basis states of the phase space representation. Generalization of the approach for multidimensional cases is shown. Examples of applications are given.

10 pages

References in corpus (2)

• Wigner phase space distribution as a wave function
• Quantum Mechanics in Phase Space

Cited by in corpus (6)

• Dispersion Operators Algebra and Linear Canonical Transformations
• Phase space density limitation in laser cooling without spontaneous emission
• Study on linear canonical transformation in a framework of a phase space representation of quantum mechanics
• Properties of Elementary Fermions of the Standard Model deduced from Linear Canonical Transformations
• Derivation of equations for scalar and fermion fields using properties of dispersion-codispersion operators
• Study on a Spinorial Representation of Linear Canonical Transformations