Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Huadong Shifan Daxue xuebao. Ziran kexue ban

A Study of Coherent States and Their Propagator

Zhongyan Shen

Published Jan 1, 1984• 0 citations
OpenAlex

Abstract

Using a transformation of pictures and representations,we have obtained several formulas for the coherent states in Hesenberg pictures and coordinate representations as follows: The relation between the coherent states propagator and general Feynman propa- gator is further developed:

Related papers

CLASSICAL OPTICAL TRANSFORMS STUDIED IN THE CONTEXT OF QUANTUM OPTICS VIA THE ROUTE OF DEVELOPING DIRAC'S SYMBOLIC METHOD

Hong-Yi Fan, Lu Hai-Liang

Via the route of developing Dirac's symbolic method and following Dirac's assertion: "⋯ for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory", we find the generalized Fresnel operator (GFO) corresponding to the generalized Fresnel transform (GFT) in classical optics. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in quantum optics. With the aid of entangled state representation the entangled Fresnel transform is proposed; new eigenfunctions of the complex fractional Fourier transform and fractional Hankel transform are obtained; the two-variable Hermite eigenmodes of light propagation are used in studying the Talbot effect in quadratic-index media; the complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Moreover, quantum optical version of classical z-transforms is obtained on the basis of the eigenvector of creation operator. Throughout our discussions, the coherent state, squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used.

International Journal of Modern Physics B•Feb 20, 2005•19 citations

From the coherent state path integral to a semiclassical initial value representation of the quantum mechanical propagator

Frank Großmann, Ademir Luiz Xavier Junior

Physics Letters A•Jul 1, 1998•70 citations

Feynman’s propagator in Schwinger’s picture of Quantum Mechanics

Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort +3 more

A novel derivation of Feynman’s sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. It is shown that such construction corresponds to the GNS representation of a natural family of states called Dirac–Feynman–Schwinger (DFS) states. Such states are obtained from a q-Lagrangian function [Formula: see text] on the groupoid of configurations of the system. The groupoid of histories of the system is constructed and the q-Lagrangian [Formula: see text] allows us to define a DFS state on the algebra of the groupoid. The particular instance of the groupoid of pairs of a Riemannian manifold serves to illustrate Feynman’s original derivation of the propagator for a point particle described by a classical Lagrangian L.

arXiv:2109.05756•Modern Physics Letters A•Aug 30, 2021•9 citations

Heisenberg picture in quantum mechanics and linear evolutionary systems

Pasquale Nardone

A straightforward procedure is presented to derive the propagator in simple quantum systems. This approach enables us to define a state which behaves as a generalization of the well-known coherent state of the harmonic oscillator.

American Journal of Physics•Mar 1, 1993•19 citations

A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation

Chuanmei Xie, Fan Hong-Yi, Shaolong Wan

Based on the displacement-squeezing related squeezed coherent state representation | z⟩ g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula (Huygens–Fresnel integration transformation describing optical diffraction). The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz - rz * in the | z⟩ g representation, while | z⟩ g in phase space is graphically denoted by an ellipse.

Chinese Physics B•Jun 1, 2010•8 citations

Phase space representation of quantum mechanics in terms of coherent states

Michele Cini, Maurizio Serva

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B•Jul 1, 1992•1 citation
Via the route of developing Dirac's symbolic method and following Dirac's assertion: "⋯ for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory", we find the generalized Fresnel operator (GFO) corresponding to the generalized Fresnel transform (GFT) in classical optics. We derive GFO's normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in quantum optics. With the aid of entangled state representation the entangled Fresnel transform is proposed; new eigenfunctions of the complex fractional Fourier transform and fractional Hankel transform are obtained; the two-variable Hermite eigenmodes of light propagation are used in studying the Talbot effect in quadratic-index media; the complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Moreover, quantum optical version of classical z-transforms is obtained on the basis of the eigenvector of creation operator. Throughout our discussions, the coherent state, squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used.
A novel derivation of Feynman’s sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. It is shown that such construction corresponds to the GNS representation of a natural family of states called Dirac–Feynman–Schwinger (DFS) states. Such states are obtained from a q-Lagrangian function [Formula: see text] on the groupoid of configurations of the system. The groupoid of histories of the system is constructed and the q-Lagrangian [Formula: see text] allows us to define a DFS state on the algebra of the groupoid. The particular instance of the groupoid of pairs of a Riemannian manifold serves to illustrate Feynman’s original derivation of the propagator for a point particle described by a classical Lagrangian L.
Based on the displacement-squeezing related squeezed coherent state representation | z⟩ g and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula (Huygens–Fresnel integration transformation describing optical diffraction). The generalized Fresnel operator is derived by a quantum mechanical mapping from z to sz - rz * in the | z⟩ g representation, while | z⟩ g in phase space is graphically denoted by an ellipse.