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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: In this article, it is shown that there exist symmetry transformations in phase space that preserve Hamilton's canonical equations of motion for one Hamiltonian, but not for all, and that a sufficient condition for a canonical transformation to be canonical is that it preserves Hamilton's equations for all Hamiltonians quadratic in theq's andp's.
Abstract: It is shown that there exist symmetry transformations in phase space that preserve Hamilton’s canonical equations of motion for one Hamiltonian, but not for all. Examples of these « canonoid » transformations are given and their relation to canonical transformations is developed. It is demonstrated that a sufficient condition for a canonoid transformation to be canonical is that it preserve Hamilton’s equations for all Hamiltonians quadratic in theq’s andp’s.
29 citations
TL;DR: In this article, a connection between an algebraic approach to the dynamics of triatomic molecules based on the U(2) × U(3) ×U(2)-Lie algebra and the traditional description in configuration space is presented.
29 citations
TL;DR: Bambusi et al. as mentioned in this paper considered the nonlinear Schodinger equation with periodic boundary conditions on [−π,π]d,d⩾1; g is analytic and g(0,0)=Dg( 0,0) = 0; V is a potential in L2; and showed that for any integer M there exists a canonical transformation that puts the Hamiltonian in Birkhoff normal form up to a reminder of order M.
29 citations
TL;DR: In this paper, the authors apply the Consistent Discretization technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions.
Abstract: We apply the "consistent discretization" technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well-defined canonical theory that is free of constraints and where the dynamics is implemented as a canonical transformation. In the Lorentzian case, the framework appears to be naturally free of the "spikes" that plague traditional formulations. It also provides a well-defined recipe for determining the integration measure for quantum Regge calculus.
29 citations
TL;DR: In this paper, the polaronic corrections to the first excited state energies of an electron in a parabolic quantum dot are obtained variationally for the entire range of the electron-phonon coupling constant and for arbitrary confinement length using a canonical transformation method based on the Lee-Low-Pines-Gross formalism.
Abstract: The polaronic corrections to the first excited-state energies of an electron in a parabolic quantum dot are obtained variationally for the entire range of the electron-phonon coupling constant and for arbitrary confinement length using a canonical transformation method based on the Lee-Low-Pines-Gross formalism. Simple analytical results are obtained in some interesting limiting cases and for arbitrary values of the parameters the nature of the excited state is studied numerically. The theory is applied to two- and three-dimensional GaAs quantum dots to obtain information about the existence of both the effective mass and the relaxed excited states of a polaron in these systems.
29 citations