Quasipotential models of a relativistic oscillator

Atakishiev, N. M.; Mir‐Kasimov, R. M.; Nagiev, Sh. M.

doi:10.1007/bf01038009

Cited by 32 publications

(22 citation statements)

References 11 publications

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“…Quasipotential models of a relativistic oscillator were first considered in [3,4,5]. The ρ-representation or the ρn representation (|n| = 1) may also be used in a so-called generalized Schrödinger (GS) picture in which the analogs of the Schrödinger operators of a particle are independent of both the time and the space coordinates t, x in different representations [6].…”

Section: Introductionmentioning

confidence: 99%

Model of a relativistic oscillator in a generalized Schrödinger picture

Frick

2011

Annalen der Physik

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In a generalized Schrödinger picture, we consider the motion of a relativistic particle in an external field (like in the case of a harmonic oscillator). In this picture the analogs of the Schrödinger operators of the particle are independent of both the time and the space coordinates. These operators induce operators which are related to Killing vectors of the Anti de Sitter (AdS) space. We also consider the nonrelativistic limit.

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Section: Introductionmentioning

confidence: 99%

Model of a relativistic oscillator in a generalized Schrödinger picture

Frick

2011

Annalen der Physik

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“…Another realization is a quasipotential model of the relativistic oscillator; see, for example, [37], [7], and [8]. We shall discuss this model and its generalization in the next two sections.…”

Section: Expansion Formula For a Plane Wavementioning

confidence: 99%

“…As is known [7] a dynamical symmetry group for the relativistic oscillator with the Hamiltonian (12.1) is the group SU (1, 1) (or isomorphic groups SO (2, 1) ∼ Sp (2, R) ∼ SL (2, R)), whose generators are realized as the difference operators…”

Section: A Modified Relativistic Oscillatormentioning

confidence: 99%

“…For the consistent three-dimensional description of a relativistic two-particle system in quantum field theory a quasipotential approach had been formulated and, in the framework of this approach, some relativistic generalizations of the exactly solvable problems of quantum mechanics have been considered; see [37], [7], and references therein for more information. We shall discuss here a model of the (simple) relativistic oscillator described by the following Hamiltonian operator…”

Section: Propagator For the Relativistic Oscillatormentioning

confidence: 99%

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Solution of the Cauchy problem for a time-dependent Schrödinger equation

Meiler

Cordero-Soto

Suslov

2008

Journal of Mathematical Physics

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Abstract. We construct an explicit solution of the Cauchy initial value problem for the n-dimensional Schrödinger equation with certain time-dependent Hamiltonian operator of a modified oscillator. The dynamical SU (1, 1) symmetry of the harmonic oscillator wave functions, Bargmann's functions for the discrete positive series of the irreducible representations of this group, the Fourier integral of a weighted product of the Meixner-Pollaczek polynomials, a Hankel-type integral transform and the hyperspherical harmonics are utilized in order to derive the corresponding Green function. It is then generalized to a case of the forced modified oscillator. The propagators for two models of the relativistic oscillator are also found. An expansion formula of a plane wave in terms of the hyperspherical harmonics and solution of certain infinite system of ordinary differential equations are derived as a by-product.

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“…Note that the connection of the Meixner oscillator (at specific value of parameter ϕ = π 2 ) with the relativistic model of linear oscillator [52] was mentioned in the work [10]. However this connection was not obvious and the reasons of appearence of specific value of parameter ϕ = π …”

Section: Introductionmentioning

confidence: 99%