2021   03   en   p.20-27 E.I. Jafarov, A.M. Jafarova, S.M. Nagiyev, S.K. Novruzova,
The confined harmonic oscillator as an explicit solution of the position-dependent effective mass Schrodinger equation with Morrow-Brownstein Hamiltonian


Exactly-solvable confined model of the non-relativistic quantum harmonic oscillator with Morrow-Brownstein kinetic energy operator
H0=Mα(x)p̂x Mβ (x)p̂xMα(x)/2 (with 2α+β=-1) is proposed. Corresponding position-dependent effective mass Schrödinger equation in the canonical approach is solved in position representation. Explicit expressions of both wavefunctions of the stationary states and discrete e nergy spectrum have been found. It is shown that the energy spectrum has non-equidistant form and depends on both confinement parameter a and Morrow-Brownstein parameter α. Wavefunctions of the stationary states in position representation are expressed in terms of the Gegenbauer polynomials. At limit α→∞, both energy spectrum and wavefunctions recover well-known equidistant energy spectrum and wavefunctions of the stationary non-relativistic harmonic oscillator expressed by Hermite polynomials. Position dependence of the effective mass also disappears under the same limit.

Keywords: Morrow-Brownstein kinetic energy operator, confined harmonic oscillator model, exact solution, Gegenbauer polynomials, non-equidistant energy spectrum, position-dependent effective mass
PACS: 03.65.-w; 02.30.Hq; 03.65.Ge


Received: 14.07.2021


Institute of Physics, Azerbaijan National Academy of Sciences Javid ave. 131, AZ1143, Baku, Azerbaijan

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