Generalized semiconfined harmonic oscillator model with a
position-dependent effective mas
- URL: http://arxiv.org/abs/2110.10581v2
- Date: Mon, 14 Feb 2022 14:20:22 GMT
- Title: Generalized semiconfined harmonic oscillator model with a
position-dependent effective mas
- Authors: C. Quesne
- Abstract summary: It is shown that a semiconfined harmonic oscillator model with a position-dependent mass in the BenDaniel-Duke setting can be easily constructed.
A further generalization is proposed by considering a $m$-dependent position-dependent mass for $0m2$ and deriving the associated semiconfined potential.
The potential that would result from a general von Roos kinetic energy operator is presented and the examples of the Zhu-Kroemer and Mustafa-Mazharimousavi settings are briefly discussed.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: By using a point canonical transformation starting from the constant-mass
Schr\"odinger equation for the isotonic potential, it is shown that a
semiconfined harmonic oscillator model with a position-dependent mass in the
BenDaniel-Duke setting and the same spectrum as the standard harmonic
oscillator can be easily constructed and extended to a semiconfined shifted
harmonic oscillator, which could result from the presence of a uniform
gravitational field. A further generalization is proposed by considering a
$m$-dependent position-dependent mass for $0<m<2$ and deriving the associated
semiconfined potential. This results in a family of position-dependent mass and
potential pairs, to which the original pair belongs as it corresponds to $m=1$.
Finally, the potential that would result from a general von Roos kinetic energy
operator is presented and the examples of the Zhu-Kroemer and
Mustafa-Mazharimousavi settings are briefly discussed.
Related papers
- Pseudo-Hermitian extensions of the harmonic and isotonic oscillators [9.944647907864256]
We describe certain pseudo-Hermitian extensions of the harmonic and isotonic oscillators.
We explicitly solve for the wavefunctions in the position representation and also explore their intertwining relations.
arXiv Detail & Related papers (2024-08-02T17:15:17Z) - Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators.
We find conditions for their strong continuity and establish properties of their generators.
arXiv Detail & Related papers (2024-06-15T17:39:32Z) - On the validity of the rotating wave approximation for coupled harmonic oscillators [34.82692226532414]
We solve the dynamics analytically by employing tools from symplectic geometry.
We find that the squeezing present in the full Hamiltonian and in the initial state governs the deviation from the approximated evolution.
We also show that the rotating wave approximation is recovered for resonant frequencies and vanishing coupling to frequency ratio.
arXiv Detail & Related papers (2024-03-22T16:51:53Z) - Quasi-exactly solvable potentials in Wigner-Dunkl quantum mechanics [0.0]
It is shown that the Dunkl harmonic oscillator on the line can be generalized to a quasi-exactly solvable one.
The Hamiltonian of the latter can also be rewritten in a simpler way in terms of an extended Dunkl derivative.
arXiv Detail & Related papers (2024-01-09T14:44:31Z) - Rational extensions of an oscillator-shaped quantum well potential in a
position-dependent mass background [0.0]
A recently proposed quantum well model associated with a position-dependent mass can be solved by applying a point canonical transformation to the constant-mass Schr"odinger equation for the Scarf I potential.
Some more involved position-dependent mass models associated with $X$-Jacobi exceptionals are also considered.
arXiv Detail & Related papers (2023-09-20T14:46:46Z) - Slow semiclassical dynamics of a two-dimensional Hubbard model in
disorder-free potentials [77.34726150561087]
We show that introduction of harmonic and spin-dependent linear potentials sufficiently validates fTWA for longer times.
In particular, we focus on a finite two-dimensional system and show that at intermediate linear potential strength, the addition of a harmonic potential and spin dependence of the tilt, results in subdiffusive dynamics.
arXiv Detail & Related papers (2022-10-03T16:51:25Z) - Quantum vibrational mode in a cavity confining a massless spinor field [91.3755431537592]
We analyse the reaction of a massless (1+1)-dimensional spinor field to the harmonic motion of one cavity wall.
We demonstrate that the system is able to convert bosons into fermion pairs at the lowest perturbative order.
arXiv Detail & Related papers (2022-09-12T08:21:12Z) - Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via
coupled Heisenberg equations [23.87373187143897]
We study the isotropic Kitaev spin-$1/2$ model on the Bethe lattice.
We take a straightforward approach of solving Heisenberg equations for a tailored subset of spin operators.
As an example, we calculate the time-dependent expectation value of this observable for a factorized translation-invariant.
arXiv Detail & Related papers (2021-10-25T17:37:33Z) - Comment on `Exact solution of the position-dependent effective mass and
angular frequency Schr\"odinger equation: harmonic oscillator model with
quantized confinement parameter' [0.0]
In a recent paper, Jafarov, Nagiyev, Oste and Van der Jeugt, construct a confined model of the non-relativistic quantum harmonic oscillator.
By using a point canonical transformation starting from the constant-mass Schr"odinger equation for the Rosen-Morse II potential, it is shown here that similar results can be easily obtained without quantizing the confinement parameter.
arXiv Detail & Related papers (2021-05-06T14:20:06Z) - Quantum dynamics of the classical harmonic oscillator [0.0]
A correspondence is established between measure-preserving, ergodic dynamics of a classical harmonic oscillator and a quantum mechanical gauge theory on two-dimensional Minkowski space.
arXiv Detail & Related papers (2019-12-27T21:00:10Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.