2021   01   en   p.33-39 Sh.M. Nagiyev, K.Sh. Jafarova,
Generalized Hamiltonian with position-dependent mass and pseudo-Jacobi oscillator


Exactly-solvable model of the quantum harmonic oscillator is proposed. In this work we propose a new generalized Hamiltonian, to describe variable mass systems. Wave functions of the stationary states and energy spectrum of the model are obtained through the solution of the corresponding Schrödinger equation with the positive position-dependent effective mass. We have shown that the wave functions of the stationary states of the model under consideration are expressed through the pseudo Jacobi polynomials Pn (ξ; ν, N¯). The parameter a of the model is quantized in terms of N¯. As a consequence of it, the number of the its energy spectrum is finite. Under the limit a → ∞ the system recovers the known non-relativistic quantum harmonic oscillator in the quantum mechanics. We also obtained the limiting relation between the pseudo Jacobi and Hermite polynomials.

Keywords: Position-dependent effective mass, new generalized free Hamiltonian, quantum harmonic oscillator, pseudo Jacobi polynomials, non-equidistant energy levels.
PACS: 03.65.-w, 02.30.Hq, 03.65.Ge

Received: 08.02.2021


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

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