Exact solutions of an exponential type position dependent mass problem

Dong, Shi‐Hai; Huang, Wenhua; Sedaghatnia, Parisa; Hassanabadi, H.

doi:10.1016/j.rinp.2022.105294

Cited by 14 publications

(11 citation statements)

References 33 publications

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“…3 The Theory of PDM and its exact solutions Within the concept of position dependent mass, the kinetic energy with a self adjoint form is expressed in the form [23][24][25][26], ( )…”

Section: A Brief Review Of Enu Methodsmentioning

confidence: 99%

“…[21][22] and the references therein) have been investigated within the framework of PDM using the aforementioned techniques. Dong et al [23] obtained the exact solutions of the Schrodinger equation with an exponential type PDM. Amir and Iqbal [24] obtained the exact solutions of Schrodinger equation for a particle with PDM trapped inside an infinite square well (ISW).…”

Section: Introductionmentioning

confidence: 99%

“…− . However, for a special case such as 0 qr == and 1 s =− then the kinetic energy operator of equation (11) becomes, position dependent mass Schrodinger equation in one dimension takes the form[23][24][25][26],…”

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confidence: 99%

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Exact Solutions of position dependent mass Schrodinger equation with Pseudoharmonic Oscillator and its thermal properties using extended Nikiforov-Uvarov method

Ikot

Okon

Okorie

et al. 2023

Preprint

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In this work, we find the exact solution of Schrödinger wave equation for position dependent mass with pseudoharmonic oscillator using extended Nikiforov-Uvarov method. We obtained the energy-eigen equation presented in a closed and compact form and used the result to study both superstatistics and thermodynamic properties by first determining the partition function of the system. The unnormalized wave function was obtained and expressed in terms of Confluent Heun function. Using the resulting energy eigen equation, the numerical computation were computed for varying masses for with fixed physical constant potential parameter λ. The numerical result shows that the bound state energies increase with quantum states but decreases with the dependent mass m(x). The thermodynamics and superstatistics plots are also reported.

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“…3 The Theory of PDM and its exact solutions Within the concept of position dependent mass, the kinetic energy with a self adjoint form is expressed in the form [23][24][25][26], ( )…”

Section: A Brief Review Of Enu Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exact Solutions of position dependent mass Schrodinger equation with Pseudoharmonic Oscillator and its thermal properties using extended Nikiforov-Uvarov method

Ikot

Okon

Okorie

et al. 2023

Preprint

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“…1. Let us look for a solution such that mfalse(xfalse)=m0e−ax motivated from recent arguments in the context of quantum superstatistics [78], WKB approximations in quantum mechanics [54] and relativistic quantum dynamics [45,79]. Here m0=mfalse(x=0false) and a is a real parameter assumed to be too small with respect to unity.…”

Section: Some Applications Of the Generalized Schrödinger Equationmentioning

confidence: 99%

Quantum mechanics with spatial non-local effects and position-dependent mass

El-Nabulsi

Anukool

2022

Proc. R. Soc. A.

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A new higher order Schrödinger equation characterized by a position-dependent mass is introduced based on long-range spatial kernel effects and von Roos arguments. The extended Schrödinger equation depends on the sign of the moments M k , k = 0 , 1 , 2 , … and a stabilized quantum dynamic is realized for M 2 > 0 and M 4 > 0 . We have discussed its implications in several quantum mechanical systems where more than a few were raised, mainly the emergence of the quantum Pais-Uhlenbeck and the relativistic quantum harmonic oscillators besides the complex periodic potential characterized by a PT symmetry.

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“…It is found that even in the presence of KEO ambiguity some class of potential are exactly solved. On the other hand, the PDM arises in investigations of exact solutions of some kind of exponential mass distribution [19], semi-confined harmonic oscillator [20], quantum gravitational effect [21], and quantum information entropies [22].…”

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confidence: 99%

Non-Hermitian fermions with effective mass

Lima¹,

Monteiro²,

Almeida³

2023

Preprint

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In this work, we readdress the Dirac equation in the position-dependent mass (PDM) scenario. Here, one investigates the quantum dynamics of non-Hermitian fermionic particles with effective mass assuming a (1 + 1)-dimension flat spacetime.In seeking a Schrödinger-like theory with PT symmetry is appropriate to assume a complex potential. This imaginary interaction produces an effective potential purely dependent on mass distribution. Furthermore, we study the non-relativistic limit by adopting the Foldy-Wouthuysen transformation. As a result, that limit leads to an ordering equivalent to the ordering that describes abrupt heterojunctions. Posteriorly, particular cases of mass distribution also were analyzed. Thus, interesting results arise for the case of a linear PDM, which produces an effective harmonic oscillator and induces the emergence of bound states. For a hyperbolic PDM, an effective potential barrier emerges. However, in this case, the fermions behave as free particles with positive-defined energy. I. INTRODUCTIONProblems of position-dependent effective mass help us to understand impurity in crystals [1-3], and heterojunctions in semiconductors [4, 5]. Furthermore, the idea of the positiondependent effective mass (commonly called position-dependent mass or PDM) became an attractive topic for several researchers, see Refs. [6-10].The PDM concept in a non-relativistic regime is ambiguous. Indeed, this is because the momentum operator is not well defined. Therefore, it needs to symmetrize its kinetic

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Exact solutions of an exponential type position dependent mass problem

Cited by 14 publications

References 33 publications

Exact Solutions of position dependent mass Schrodinger equation with Pseudoharmonic Oscillator and its thermal properties using extended Nikiforov-Uvarov method

Exact Solutions of position dependent mass Schrodinger equation with Pseudoharmonic Oscillator and its thermal properties using extended Nikiforov-Uvarov method

Quantum mechanics with spatial non-local effects and position-dependent mass

Non-Hermitian fermions with effective mass

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