Exact solution of the position-dependent effective mass and angular frequency Schrodinger equation : harmonic oscillator model with quantized confinement parameter
| Autor: | J. Van der Jeugt, Elchin I. Jafarov, Roy Oste, Sh. M. Nagiyev |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
QUANTUM-WELLS Schrö BenDaniel– FOS: Physical sciences General Physics and Astronomy quantized confinement parameter 01 natural sciences 81Q05 ENERGY-GAP 010305 fluids & plasmas symbols.namesake position-dependent effective mass and angular frequency Effective mass (solid-state physics) harmonic oscillator Quantum mechanics 0103 physical sciences 010306 general physics Harmonic oscillator Mathematical Physics Physics Quantum Physics Angular frequency Hermite polynomials Gegenbauer polynomials Statistical and Nonlinear Physics Mathematical Physics (math-ph) confined TIME Duke kinetic energy Mathematics and Statistics Physics and Astronomy dinger equation Quantum harmonic oscillator LAYER Modeling and Simulation operator symbols associated Legendre and Gegenbauer polynomials ALGEBRAIC APPROACH Quantum Physics (quant-ph) Hamiltonian (quantum mechanics) POINT Stationary state |
| Zdroj: | JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL |
| ISSN: | 1751-8113 1751-8121 |
| 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 ∞, 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: | OpenAIRE |
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