Squeezed states and Hermite polynomials in a complex variable

DOI10.1063/1.4861932zbMath1315.81053arXiv1308.4730OpenAlexW3106147584WikidataQ116677414 ScholiaQ116677414MaRDI QIDQ5414755

Franciszek Hugon Szafraniec, Katarzyna Górska, Andrzej Horzela, Syed Twareque Ali

Publication date: 7 May 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.4730

zbMATH Keywords

Hermite polynomialsBargmann spaceHilbert spaces of entire functionsreproducing kernel spacesqueezed states

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Quantum optics (81V80) Coherent states (81R30) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Spaces of differentiable or holomorphic functions on infinite-dimensional spaces (46E50)

Related Items

Multivariate holomorphic Hermite polynomials ⋮ Holomorphic Hermite polynomials in two variables ⋮ Mittag-Leffler function and fractional differential equations ⋮ New complex function space related to both entangled state representation and spin coherent state ⋮ Two-mode squeezed state quantisation and semiclassical portraits ⋮ General construction of reproducing kernels on a quaternionic Hilbert space ⋮ Holomorphic Hermite functions in Segal-Bargmann spaces ⋮ Hermite polynomials and quasi-classical asymptotics ⋮ Coherence, Squeezing and Entanglement: An Example of Peaceful Coexistence ⋮ Bargmann-type transforms and modified harmonic oscillators ⋮ Geometric dynamics of a harmonic oscillator, arbitrary minimal uncertainty states and the smallest step 3 nilpotent Lie group ⋮ Mathematical work of Franciszek Hugon Szafraniec and its impacts ⋮ Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics

Uses Software

• Equator

Cites Work

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