A conjugate for the Bargmann representation

Abstract

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 ${\hat{a}}^{†}$ and $\hat{a}$ 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 ${\hat{a}}^{†}$ and $\hat{a}$ 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.

15 pages

References in corpus (6)

• Semiclassical Propagation of Wavepackets with Real and Complex Trajectories
• A Uniform Approximation for the Coherent State Propagator using a Conjugate Application of the Bargmann Representation
• Coherent State Path Integrals in the Weyl Representation
• Phase space caustics in multi-component systems
• Controlling Phase Space Caustics in the Semiclassical Coherent State Propagator
• Evaluation of the semiclassical coherent state propagator in the presence of phase space caustics

Cited by in corpus (3)

• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• Semiclassics around a phase space caustic: an illustration using the Nelson Hamiltonian
• Coherent-State Overcompleteness, Path Integrals, and Weak Values