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arXiv:quant-ph/0505155 · Physical Review Letters

Uniform Approximation for the Coherent-State Propagator Using a Conjugate Application of the Bargmann Representation

A. D. Ribeiro, Marcel Novaes, Marcus A. M. de Aguiar

Published Jul 29, 2005• 19 citations
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Abstract

We propose a conjugate application of the Bargmann representation of quantum mechanics. Applying the Maslov method to the semiclassical connection formula between the two representations, we derive a uniform semiclassical approximation for the coherent-state propagator which is finite at phase space caustics.
DOI
10.1103/physrevlett.95.050405

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In the Bargmann representation of quantum mechanics, physical states are mapped into entire functions of a complex variable z *, whereas the creation and annihilation operators and play the role of multiplication and differentiation with respect to z *, respectively. In this paper we propose an alternative representation of quantum states, conjugate to the Bargmann representation, where the roles of and are reversed, much like the roles of the position and momentum operators in their respective representations. We derive expressions for the inner product that maintain the usual notion of distance between states in the Hilbert space. Applications to simple systems and to the calculation of semiclassical propagators are presented.