2021   01   az   p.50-58 E.I. Jafarov, A.M. Mammadova and N.F. Mammadova,
Exact solution of the one-dimensional quantum box-like harmonic oscillator model under the von roos kinetic energy operator		  pdf 

ABSTRACT

We propose exactly-solvable model of the one-dimensional quantum harmonic oscillator in the framework of the effective mass formalism varying with position. Analytical expression of the position-dependent effective mass is chosen by such a way that it exhibits effect of quantization and can change behaviour of the potential from harmonic oscillator to quantum box with non-quadratic profile. Wave functions of the stationary states of the oscillator model under study have been obtained by solving exactly corresponding Schrödinger equation, which free Hamiltonian is defined via the von Roos kinetic energy operator. Analytical expression of the wave function is described by the pseudo Jacobi polynomials, whereas obtained energy spectrum is discrete, non-equidistant and finite. It is shown that both energy spectrum and wave function completely recover known expressions of the so-called Hermite oscillator equidistant energy spectrum and wave function of the stationary states under the limit N→∞.

Keywords: Coordinate-dependent effective mass, quantum harmonic oscillator, pseudo Jacobian polynomials, non-equidistant energy spectrum
PACS: 03.65.-w, 02.30.Hq, 03.65.Ge

DOI:-

Received: 03.03.2021

AUTHORS & AFFILIATIONS

Institute of Physics of Azerbaijan National Academy of Sciences, 131 H. Javid ave, Baku, AZ-1143, Azerbaijan
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