Abstract
An explicit phase space representation of the wave function is build based on a wavelet transformation. The wavelet transformation allows us to understand the relationship between s − ordered Wigner function, (or Wigner function when s = 0), and the Torres-Vega-Frederick’s wave functions. This relationship is necessary to find a general solution of the Schrödinger equation in phase-space.
Highlights
The Wigner function,[1] introduced in 1932, was the first attempt to built a phase-space version of quantum mechanics, and serve as a phase-space distribution alternative to the density operator
An explicit phase space representation of the wave function is build based on a wavelet transformation
This relationship is necessary to find a general solution of the Schrödinger equation in phase-space
Summary
The Wigner function,[1] introduced in 1932, was the first attempt to built a phase-space version of quantum mechanics, and serve as a phase-space distribution alternative to the density operator. The main objective of this article is to build an explicit phase-space representation of the wave function using a wavelet transformation.[15] the article will be organized around the central theme of the wavelet transformation, which allows us to obtain and arbitrary phase-space wave function from coordinate one, with the key observation that mother wavelet and its argument can be obtained as a generalization of the explicit state vector |Γ⟩. The idea of this method is based on the generalization of the explicit state vector |Γ⟩.
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