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Canonical transformation
About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.
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TL;DR: The extended Wick's theorem for fermion operators, which is used to compute matrix elements of an arbitrary operator between two different quasiparticle vacuums, is reformulated to deal with quasips expanded in a finite single particle basis not closed under the canonical transformation relating them.
Abstract: The extended Wick's theorem for fermion operators, which is used to compute matrix elements of an arbitrary operator between two different quasiparticle vacuums, is reformulated to deal with quasiparticle vacuums expanded in a finite single particle basis not closed under the canonical transformation relating them. A new expression for the overlap of those quasiparticle vacuums is also given.
39 citations
TL;DR: In this article, the authors considered the usual Jaynes-cummings model in the presence of an external classical field and derived exact solutions for the time-dependent dynamical operators.
38 citations
TL;DR: In this article, Birkhoff's canonical transformation at an equilibrium of elliptic type with no internal resonance can be built explicitly and recursively, without partial inversions or substitutions, by means of Lie transforms.
Abstract: : Birkhoff's normalizing canonical transformation at an equilibrium of elliptic type with no internal resonance can be built explicitly and recursively, without partial inversions or substitutions, by means of Lie transforms. Invariant sections and ordinary families of periodic orbits for truncated normalized systems are analyzed in detail.
38 citations
TL;DR: In this article, the low-lying levels of an electron interacting with a quantized lattice vibration field were studied, where the wave functions were assumed to be a product of electron and lattice functions in the new variables.
38 citations
TL;DR: In this paper, the authors investigated the quantum and classical transformation properties of two-dimensional isotropic and anisotropic uncoupled harmonic oscillators. Butler et al. used a simple mapping to derive the action-angle variables appropriate for normal, local, and precessional motion of an arbitrary m:n resonance, and compared the corresponding quantum mechanical wave functions and phase space densities.
Abstract: This paper addresses the general problem of zeroth order representation of resonant dynamics. We investigate the classical, quantum mechanical, and semiclassical transformation properties of two‐dimensional isotropic and anisotropic uncoupled harmonic oscillators. The classical and quantal theories are presented in a manner that emphasizes the strong correspondence between the two, and in particular, the SU(2) symmetry exhibited by both the classical and quantum oscillators. The classical canonical transformations relating the action‐angle variables appropriate for normal, local, and precessional motion of the isotropic oscillator are derived by explicit calculation of the generating functions. By employing a simple mapping relating the anisotropic and isotropic oscillators, expressions for action‐angle variables appropriate for the topology of an arbitrary m:n resonance are determined. The resulting invariant tori are compared with the corresponding quantum mechanical wave functions and phase space densities. The relationship between the classical and quantum mechanical theories is illustrated by determining semiclassical approximations to the unitary transformation matrix elements, which are given in terms of the classical generating functions. Applications to problems of current interest, such as the adiabatic switching method for semiclassical quantization of nonseparable systems, are briefly discussed.This paper addresses the general problem of zeroth order representation of resonant dynamics. We investigate the classical, quantum mechanical, and semiclassical transformation properties of two‐dimensional isotropic and anisotropic uncoupled harmonic oscillators. The classical and quantal theories are presented in a manner that emphasizes the strong correspondence between the two, and in particular, the SU(2) symmetry exhibited by both the classical and quantum oscillators. The classical canonical transformations relating the action‐angle variables appropriate for normal, local, and precessional motion of the isotropic oscillator are derived by explicit calculation of the generating functions. By employing a simple mapping relating the anisotropic and isotropic oscillators, expressions for action‐angle variables appropriate for the topology of an arbitrary m:n resonance are determined. The resulting invariant tori are compared with the corresponding quantum mechanical wave functions and phase space densi...
37 citations