2021   04   az   p.22-29 A.M. Mammadova,
Exact solution of the quantum harmonic oscillator described by Gora-Williams kinetic energy operator in the external gravitational field		  pdf 

ABSTRACT

An exactly-solvable confined model of a nonrelativistic quantum harmonic oscillator is proposed in the framework of the formalism of an effective mass varying with position. Exact expressions for the wavefunctions of the considered oscillator model have been obtained by solving the corresponding Schrödinger equation. When the effective mass varies by position, in order to preserve the Hermitian properties of the harmonic oscillator model, the Gora-Williams kinetic energy operator is employed, and it is shown that the wavefunctions of stationary states of the studied quantum system are described by Jacobi polynomials, and the energy spectrum is discrete, non-equidistant, finite and depends on the external gravitational field. In the special case, when the external gravitational field equals to zero, the model under the study reduces into a confined model of a nonrelativistic quantum harmonic oscillator, the wavefunctions of which are described by Gegenbauer polynomials, and in the limit case, when the confinement parameter a → ∞, the quantum system under study completely restores the nonrelativistic quantum harmonic oscillator in the external field, wavefunctions of stationary states of which are described by Hermite polynomials.

Keywords: Gora-Williams kinetic energy operator, quantum harmonic oscillator, confinement model, external gravitational field, coordinate-dependent effective mass
PACS: 03.65.-w; 02.30.Hq; 03.65.Ge

DOI:-

Received: 18.10.2021

AUTHORS & AFFILIATIONS

Institute of Physics of Azerbaijan National Academy of Sciences, 131 H. Javid ave, Baku, AZ-1143, Azerbaijan
E-mail: a.mammadova@physics.science.az 		REFERENCIES

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