Wavefunctions on phase space

Smith, T.B. (2006). Wavefunctions on phase space. Journal of Physics A: Mathematical and General, 39(6) pp. 1469–1484.

DOI: https://doi.org/10.1088/0305-4470/39/6/019

Abstract

Theories of Torres-Vega and Fredrick (1993 J. Chem. Phys. 98 3103), Harriman (1994 J. Chem. Phys. 100 3651) and Ban (1998 J.Math. Phys. 39 1744), in which phase space points (p,q) are used as configurational variables to formulate quantum mechanics are considered from the standpoint of a class of quantization schemes associating phase space functions with operators. The connection between these schemes and the theories given by others is made by means of augmented wavefunctions psi(lambda;p,q), where lambda = 0 corresponds to the ordering of Wigner and Weyl. For that case we use these functions to define a family of positive operator-valued measures for the phase angle of an harmonic oscillator.

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