Exactly Soluble Harmonic Oscillator for a Particular Form of Time and Coordinates-Dependent Mass

Jannussis, A.; Karayannis, G.; Παναγόπουλος, Παναγιώτης; Papatheou, V.; Symeonidis, M; Vavougios, D.; Siafarikas, P. D.; Zisis, V.

doi:10.1143/jpsj.53.957

Cited by 11 publications

(9 citation statements)

References 18 publications

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“…Under the setting (27) the coefficients ϕ 2 and ϕ 3 vanish, as required in (23) and (24); furthermore, we infer from (20) that ϕ 5 = i, which satisfies (26). Therefore equation (16) reduces to the form…”

Section: Solution Of the Constraints And The Explicit Transformationmentioning

confidence: 90%

“…Exact solutions for masses depending on time and positions have only been obtained in [16]. Note that in the latter reference the Hamiltonian (2) with α = −1, β = γ = 0 is used, which is not equivalent to the Hamiltonian (3) that we use here.…”

Section: Hamiltonian and Tdsementioning

confidence: 99%

“…Since we are looking for a form-preserving transformation, we want the transformed equation (16) to take the form of a TDSE in the new coordinates (u, v). Before setting up constraints on the ϕ j , we define the mass in the transformed TDSE as M(x, t) =M (u, v).…”

Section: Performing the General Transformation And Setting Up The Conmentioning

confidence: 99%

“…However, to the best of our knowledge, the fully time-dependent case (i.e. the potential depends on time) has not been studied thoroughly yet, in fact, it has only been considered in [16] (harmonic oscillator and particular form of effective mass) and [17] (transformations of conventional Hamiltonians with effective mass). Therefore, the aim of this note is to take a powerful solution method for the conventional (with non-effective mass) Schrödinger equation and make it work for time-dependent problems with effective mass.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

Schulze-Halberg

2005

Open Physics

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Abstract:We study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.

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Section: Solution Of the Constraints And The Explicit Transformationmentioning

confidence: 90%

Section: Hamiltonian and Tdsementioning

confidence: 99%

Section: Performing the General Transformation And Setting Up The Conmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

Schulze-Halberg

2005

Open Physics

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“…There are a lot of studies devoted to a quantum harmonic oscillator with a position-dependent effective mass [19,24,29,[42][43][44][45][46][47][48]. In these studies, a deformation of the harmonic oscillator potential (1) occurs through the replacement of the constant effective mass m 0 by a position-dependent effective mass M(x), as a consequence of the relation with the force constant k, given by eq.…”

Section: Introductionmentioning

confidence: 99%

Exact solution of the position-dependent effective mass and angular frequency Schrödinger equation: harmonic oscillator model with quantized confinement parameter

Jafarov,

Nagiyev,

Oste

et al. 2020

Preprint

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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.

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Difference equations in the Lie-admissible formulation

Jannussis

1985

Lett. Nuovo Cimento

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Exactly Soluble Harmonic Oscillator for a Particular Form of Time and Coordinates-Dependent Mass

Cited by 11 publications

References 18 publications

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

Exact solution of the position-dependent effective mass and angular frequency Schrödinger equation: harmonic oscillator model with quantized confinement parameter

Difference equations in the Lie-admissible formulation

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