Journal of Computational Chemistry
Journal of Computational Chemistry
5 years ago

The eigenvalue problem in phase space

The eigenvalue problem in phase space
Leon Cohen
We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc. We use the Wigner distribution to formulate the standard quantum mechanical eigenvalue problem in quantum phase space. We show that psi-representability conditions must be imposed to extract the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distribution functions.

Publisher URL: http://onlinelibrary.wiley.com/resolve/doi

DOI: 10.1002/jcc.24884

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