97-200 Brian C. Hall

Quantum Mechanics in Phase Space (56K, AMS-Latex) Apr 9, 97

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Abstract. This paper describes a phase space representation for quantum mechanics of a system whose configuration space is a compact Lie group. The phase space Hilbert space is an L^2 space of holomorphic functions, and is connected to the configuration space Hilbert space by a generalization of the Segal-Bargmann transform. Several aspects of the phase space representation and the transform are discussed, including an inversion formula, a version of the uncertainty principle, and a description of how Schrodinger operators act in the phase space representation. This paper is expository and will appear in Proceedings of the Summer Research Conference on Quantization, M. Rieffel, ed., AMS Contemporary Mathematics.

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