Self‐dual phase‐space representation of quantum mechanics and the variational principle

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AbstractThe important duality problem of phase‐space representations of quantum mechanics is discussed and the class of self‐dual representations is established. It is shown that self‐dual phase‐space representations may be endowed with a Hilbert space structure resembling the standard picture of quantum mechanics. A stationary variational principle is then formulated, enabling one to solve eigenproblems of observables directly in phase space. A modified, more usable form of this variational principle is also given together with an example of practical application to the 1D Coulomb system. © 1994 John Wiley & Sons, Inc.