| Autor: |
Jafarov, E. I., Nagiyev, S. M., Oste, R., Van der Jeugt, J. |
| Rok vydání: |
2020 |
| Předmět: |
|
| Zdroj: |
J. Phys. A: Math. Theor. 53 (2020) 485301 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1088/1751-8121/abbd1a |
| Popis: |
We present an exact solution of a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent on the position. The free Hamiltonian of the proposed model has the form of the BenDaniel--Duke kinetic energy operator. The position-dependency of the mass and the angular frequency is such that the homogeneous nature of the harmonic oscillator force constant $k$ and hence the regular harmonic oscillator potential is preserved. As a consequence thereof, a quantization of the confinement parameter is observed. It is shown that the discrete energy spectrum of the confined harmonic oscillator with position-dependent mass and angular frequency is finite, has a non-equidistant form and depends on the confinement parameter. The wave functions of the stationary states of the confined oscillator with position-dependent mass and angular frequency are expressed in terms of the associated Legendre or Gegenbauer polynomials. In the limit where the confinement parameter tends to $\infty$, both the energy spectrum and the wave functions converge to the well-known equidistant energy spectrum and the wave functions of the stationary non-relativistic harmonic oscillator expressed in terms of Hermite polynomials. The position-dependent effective mass and angular frequency also become constant under this limit. |
| Databáze: |
arXiv |
| Externí odkaz: |
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