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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 paper, it was shown that a transformation to a new Hamiltonian independent of position is in general impossible using a trans-formation satisfying this requirement; the best that can be done being a Hamiltonian which is almost everywhere in normal form, but which retains potential barriers of infinitesimal width to reflect trapped particles.
Abstract: The topological constraints imposed on a canonical transformation by the requirement of continuous connection to the identity are considered. In the case of a particle interacting with a periodic potential, it is shown that a transformation to normal form (new Hamiltonian independent of position) is in general impossible using a trans- formation satisfying this requirement; the best that can be done being a transformation to a Hamiltonian which is almost everywhere in normal form, but which retains potential barriers of infinitesimal width to reflect trapped particles. A new Hamiltonian-Jacobi theory based on Lie operator techniques is presented and its relation to the usual theory established. It is suggested that the new method enables the motion of a particle in a random potential to be transformed into an almost Markovian random walk.
12 citations
TL;DR: In this article, a simple geometrical interpretation of classical W-transformations as deformations of constant energy surfaces by canonical transformations on a two-dimensional phase space is given.
12 citations
TL;DR: In this paper, a novel algorithm is provided to couple a Galilean invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and canonical transformation of the original fields.
Abstract: A novel algorithm is provided to couple a Galilean invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and canonical transformation of the original fields. That the twin requirements are fulfilled is ensured by a new field, the existence of which was demonstrated recently from Galilean gauge theory. The ambiguities and anomalies concerning the recovery of Galilean symmetry in the flat limit of spatial non relativistic diffeomorphic theories, reported in the literature, are focused and resolved from a new angle.
12 citations
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TL;DR: In this paper, a general point canonical transformation is applied by using a free parameter to obtain the energy eigenvalues of the bound states and corresponding wave functions for target potentials as a function of the free parameter.
Abstract: PT-symmetric solutions of Schrodinger equation are obtained for the Scarf and generalized harmonic oscillator potentials with the position-dependent mass. A general point canonical transformation is applied by using a free parameter. Three different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.
12 citations
12 citations