Semi-infinite Quantum Wells In a Position-Dependent Mass Background

Quesne, Christiane

doi:10.1007/s40509-022-00291-z

Cited by 3 publications

(3 citation statements)

References 53 publications

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“…Various methods have been advocated in the literature for the exact analytical solution of the Schrödinger equation. For instance, point canonical transformations have played a significant role in the investigation of different formulations of semi-infinite quantum wells for PDM systems [12]. Other useful techniques for solving the Schrödinger equation are listed in [13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Energy spectrum and zero-temperature magnetic functions of a position-dependent mass system in a Pöschl-Teller-type potential constrained by a vector magnetic potential field

Eyube,

Notani,

Wadata

et al. 2023

Phys. Scr.

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In this work, the position-dependent mass Schrödinger equation is solved with the Pöschl-Teller-like potential in the presence of magnetic and Aharonov-Bohm (AB) flux fields. BenDaniel-Duke ambiguity parameter ordering is used to formulate the Hamiltonian operator for the system. An approximate analytical equation of the bound-state energy spectrum is obtained using the parametric Nikiforov-Uvarov solution technique along with a Pekeris-like approximation scheme. With the aid of the obtained equation for the energy levels, analytical formulas of magnetization and magnetic susceptibility at zero-temperature are derived and subsequently used to predict the physical properties of diatomic substances including the ground state H2, HCl, CO and LiH molecules. The expression for the bound-state-energy spectrum is used to generate numerical data for the molecules. The computed energy eigenvalues agree with the literature on diatomic molecules. The study revealed that in the absence of the external fields, the energy eigenvalues and magnetic susceptibility of the system are degenerate. However, with only a low intensity AB field, the degeneracy is completely eliminated from the energy states of the molecules.

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Section: Introductionmentioning

confidence: 99%

Energy spectrum and zero-temperature magnetic functions of a position-dependent mass system in a Pöschl-Teller-type potential constrained by a vector magnetic potential field

Eyube,

Notani,

Wadata

et al. 2023

Phys. Scr.

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show abstract

“…Among them, one of the most powerful is the point canonical transformation (PCT) applied to an exactly-solvable constant-mass Schrödinger equation [22,23]. Recently, such an approach has proved its efficiency again [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Rational extensions of an oscillator-shaped quantum well potential in a position-dependent mass background

Quesne

2023

Phys. Scr.

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We show that a recently proposed oscillator-shaped quantum well model associated with a position-dependent mass can be solved by applying a point canonical transformation to the constant-mass Schrödinger equation for the Scarf I potential. On using the known rational extension of the latter connected with X1-Jacobi exceptional orthogonal polynomials, we build a rationally-extended position-dependent mass model with the same spectrum as the starting one. Some more involved position-dependent mass models associated with X2-Jacobi exceptional orthogonal polynomials are also considered.

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“…For notable recent literature in the field, we refer to. [12][13][14][15][16][17][18][19][20][21][22][23][24] The PDM opens a new possibility, which is going to be explored in this paper. In particular, we are going to show how, using PDM, particles can be coupled through the kinetic part of the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

A Non‐Standard Coupling Between Quantum Systems Originated From Their Kinetic Energy

Shushi

2023

Annalen der Physik

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In standard quantum mechanics, the coupling between quantum systems is described by a potential interaction term in the Hamiltonian. This type of coupling is well‐rooted in nature and shapes the universe around us, from the interactions between single photons to the attractive force between atoms that forms molecules. Quantum mechanics does not forbid other kinds of interactions to take place. In this paper, a non‐standard quantum coupling between quantum systems is proposed, originated from the kinetic energy rather than the potential interaction in the Hamiltonian. Unlike the potential‐based coupling, the proposed coupling changes the fundamental structure of quantum mechanics in the form of modified uncertainty relations that are shaped by the coupling between the particles in the system. Two prototypical examples of non‐standard systems that perform such kinetic‐based coupling are presented. In the first example, it considers a particle confined in a heterostructure, such as a quantum dot, where the coupling is between the particle and dynamic walls that determine the size of the heterostructure. The second example involves a particle in a 3D heterostructure with coupling between its position axes. It then discusses several future implications of the proposed type of non‐standard coupling.

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Semi-infinite Quantum Wells In a Position-Dependent Mass Background

Cited by 3 publications

References 53 publications

Energy spectrum and zero-temperature magnetic functions of a position-dependent mass system in a Pöschl-Teller-type potential constrained by a vector magnetic potential field

Energy spectrum and zero-temperature magnetic functions of a position-dependent mass system in a Pöschl-Teller-type potential constrained by a vector magnetic potential field

Rational extensions of an oscillator-shaped quantum well potential in a position-dependent mass background

A Non‐Standard Coupling Between Quantum Systems Originated From Their Kinetic Energy

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