An integral transform related to quantization
- 1 August 1980
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 21 (8) , 2080-2090
- https://doi.org/10.1063/1.524702
Abstract
We study in some detail the correspondence between a function f on phase space and the matrix elements. (Qf)(a,b) of its quantized Qf between the coherent states ‖ a〉 and ‖ b〉. It is an integral transform: Qf(a,b) = F{a,b ‖ v}f(v) dv, which resembles in many ways the integral transform of Bargmann. We obtain the matrix elements of Qf between harmonic oscillator states as the Fourier coefficients of f with respect to an explicit orthonormal system.Keywords
This publication has 18 references indexed in Scilit:
- Deformation theory and quantization. I. Deformations of symplectic structuresPublished by Elsevier ,2004
- New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representationPramana, 1978
- Heat equation on phase space and the classical limit of quantum mechanical expectation valuesCommunications in Mathematical Physics, 1976
- Parity operator and quantization of δ-functionsCommunications in Mathematical Physics, 1976
- Orbits of the rotation group on spin statesJournal of Mathematical Physics, 1974
- Ordered Expansions in Boson Amplitude OperatorsPhysical Review B, 1969
- Diagonal Coherent-State Representation of Quantum OperatorsPhysical Review Letters, 1967
- The C*-algebras of a free Boson fieldCommunications in Mathematical Physics, 1965
- The action option and a Feynman quantization of spinor fields in terms of ordinary c-numbersAnnals of Physics, 1960
- Die Eindeutigkeit der Schrödingerschen OperatorenMathematische Annalen, 1931