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Springer eBooks

Weyl Rule and Pseudo-Differential Operators for Arbitrary Operators

Leon W. Cohen

Published Jan 1, 2011• 0 citations
Publisher
DOI
10.1007/978-3-0348-0049-5_15

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Quantum mechanics may be formulated in pseudo-phasespace in the Weyl picture. The semiclassical expression for the Weyl transform of the usual time evolution operator is evaluated by summing over paths a semiclassical approximation for a new propagator in pseudo-phasespace. As an example the Bohr-Sommerfeld quantisation rule is recovered. The new propagator may in principle be used to construct other interesting quantities, such as the propagator governing the time evolution of the Wigner function.