Abstract
Exactly-solvable confined model of the nonrelativistic quantum harmonic oscillator is proposed. Its position-dependent effective mass Hamiltonian is defined via the von Roos kinetic energy operator. The confinement effect to harmonic oscillator potential is included as a result of certain behaviour of the position-dependent effective mass. The corresponding Schrodinger equation in the canonical approach is exactly solved and it is shown that the discrete energy spectrum of the system under consideration depends on the confinement parameter a, von Roos parameters α, β, γ and has a non-equidistant form. Wave functions of the stationary states of the model are expressed through the Gegenbauer polynomials. The limit a → ∞ recovers both equidistant energy spectrum and wave functions of the stationary nonrelativistic harmonic oscillator expressed by Hermite polynomials.
Published Version
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