Quantum groups, coherent states, squeezing and lattice quantum mechanics

Journal Article · Sat Jul 01 00:00:00 EDT 1995 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1995.1055· OSTI ID:165575

Celeghini, E ^[1]; De Martino, S; De Siena, S ^[2]; Rasetti, M ^[3]; Vitiello, G ^[2]

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1. Dipartimento di Fisica, Universita di Firenze and INFN-Firenze, I-50125 Firenze (Italy)
2. Dipartimento di Fisica, Universita di Salerno and INFN-Napoli, I 84100 Salerno (Italy)
3. Dipartimento di Fisica and Unita INFM Politecnico di Torino, I 10129 Turin (Italy)

By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg algebra, {ital q}-WH, into the theory of entire analytic functions. The {ital q}-WH algebra operators are realized in terms of finite difference operators in the {ital z} plane. In order to exhibit the relevance of our study, several applications to different cases of physical interest are discussed; squeezed states and the relation between coherent states and theta functions on one side, and lattice quantum mechanics and Bloch functions on the other, are shown to find a deeper mathematical understanding in terms of {ital q}-WH. The role played by the finite difference operators and the relevance of the lattice structure in the completeness of the coherent states system suggest that the quantization of the WH algebra is an essential tool in the physics of discretized (periodic) systems. {copyright} 1995 Academic Press, Inc.

• OSTI ID: 165575
• Journal Information: Annals of Physics (New York), Vol. 241, Issue 1; Other Information: PBD: Jul 1995
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
QUANTUM MECHANICS
GROUP THEORY
ANALYTIC FUNCTIONS
BLOCH THEORY
EIGENSTATES
FINITE DIFFERENCE METHOD
FOCK REPRESENTATION