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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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15 Jul 1985-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this paper, relations between elements of transfer matrices are derived from the fact that the motion of charged particles from one profile plane to another can be described as a canonical transformation.
Abstract: Relations are derived between elements of transfer matrices. These relations result from the fact that the motion of charged particles from one profile plane to another can be described as a canonical transformation. The derived four first order relations are already known. Similarly, the higher order relations are very useful to check results of numerical ion optical calculations.
50 citations
TL;DR: A general theory of the realizations of Lie groups by means of canonical transformations in classical mechanics is given in this paper, which is the analog to that of the characterization of the projective representations in quantum mechanics considered by Wigner, Bargmann, and others in the case of the Galilei and the Lorentz group.
Abstract: A general theory of the realizations of Lie groups by means of canonical transformations in classical mechanics is given. The problem is the analog to that of the characterization of the projective representations in quantum mechanics considered by Wigner, Bargmann, and others in the case of the Galilei and the Lorentz group. However, no application to particular groups is given in this paper.It turns out that the generators yτ of the infinitesimal transformations in a canonical realization of a Lie group G satisfy relations of the form {yρ, yσ} = cρστyτ + dρσ, where cρστ are the structure constands of G and dρσ are constants depending on the particular realization.It also turns out that any canonical realization of G can be reduced to a fundamental typical form by means of a constant canonical transformation in the phase space of the system. This typical form allows one to obtain a complete characterization of all the possible canonical realizations of G. Once a suitable definition of ``irreducible'' can...
50 citations
TL;DR: In this article, an analysis of all the consequences of the extended second Noether theorem in the second-order formalism is made, and an answer to the Dirac conjecture is given for this class of singular Lagrangians.
Abstract: After the definition of a class of well-behaved singular Lagrangians, an analysis of all the consequences of the extended second Noether theorem in the second-order formalism is made. The phase-space reformulation contains arbitrary first- and second-class constraints. An answer to the problem of the Dirac conjecture is given for this class of singular Lagrangians. By using the concepts of function groups and of the associated Shanmugadhasan canonical transformations, an attempt is made to arrive at a global formulation of the theorem, in which the original invariance under an “infinite continuous group” of transformations is replaced by weak quasi-invariance under an “infinite continuous group ,” whose algebra is an involutive distribution of Lie-Backlund vector fields generating the Noether transformations. Its phase-space counterpart is the involutive distribution associated with a special function group Ḡpm, which contains a function subgroup Ḡp connected (when in canonical form) to the Shanmugadhasan canonical transformations. Also, the various possible first-order formalisms are analyzed.
50 citations
TL;DR: In this article, exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation.
Abstract: Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical transforma- tion is introduced by using a free parameter. Two 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.
50 citations
TL;DR: The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described in this article, where the reference potentials are used as reference to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position dependent mass settings.
Abstract: The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Poschl-Teller and Hulthen potentials are used as reference potentials to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position-dependent mass settings.
50 citations