A systematic procedure to study one-dimensional Schrödinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting situation in that, in the presence of a mass background, formation of bound states is signalled. We also discuss coordinate-transformed, constant-mass Schrödinger equation, its matching with the PDEM form and the consequent decoupling of the ambiguity parameters. This provides a unified approach to many exact results known in the literature, as well as to a lot of new ones.

B BAGCHI

P GORAIN

C QUESNE

R ROYCHOUDHURY

Fulltext

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Modern Physics Letters A

We study a generalized scheme of Swanson Hamiltonian from a second-derivative pseudo-supersymmetric approach. We discuss plausible choices of the underlying quasi-Hamiltonian and consider the viability of applications to systems like the isotonic oscillator and CPRS potential. © 2015 World Scientific Publishing Company.

International Journal of Modern Physics A

A generalized Swanson Hamiltonian in a second-derivative pseudo-supersymmetric framework

We examine the analytical structure of the nonlinear Lienard oscillator and show that it is a bi-Hamiltonian system depending upon the choice of the coupling parameters. While one has been recently studied in the context of a quantized momentum-dependent mass system, the other Hamiltonian also reflects a similar feature in the mass function and also depicts an isotonic character. We solve for such a Hamiltonian and give the complete solution in terms of a confluent hypergeometric function. (C) 2015 AIP Publishing LLC.

Journal of Mathematical Physics

On quantized Lienard oscillator and momentum dependent mass

We examine the analytical structure of the nonlinear Liénard oscillator and show that it is a bi-Hamiltonian system depending upon the choice of the coupling parameters. While one has been recently studied in the context of a quantized momentum-dependent mass system, the other Hamiltonian also reflects a similar feature in the mass function and also depicts an isotonic character. We solve for such a Hamiltonian and give the complete solution in terms of a confluent hypergeometric function. © 2015 AIP Publishing LLC.

On quantized LiÃ©nard oscillator and momentum dependent mass

This paper examines the features of a generalized position-dependent mass Hamiltonian Hm in a supersymmetric framework in which the constraints of pseudo-Hermiticity and [formula omitted] are naturally embedded. Different representations of the charge operator are considered that lead to new mass-deformed superpotentials [formula omitted] which are inherently [formula omitted]-symmetric. The qualitative spectral behavior of Hm is studied and several interesting consequences are noted. © 2013, American Institute of Physics. All rights reserved.

[formula omitted]-conserved effective mass Hamiltonians through first and higher order charge operator [formula omitted] in a supersymmetric framework

This paper examines the features of a generalized position-dependent mass Hamiltonian H-m in a supersymmetric framework in which the constraints of pseudo-Hermiticity and CPT are naturally embedded. Different representations of the charge operator are considered that lead to new mass-deformed superpotentials W-m(x) which are inherently PT-symmetric. The qualitative spectral behavior of H-m is studied and several interesting consequences are noted. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4792472]

CPT-conserved effective mass Hamiltonians through first and higher order charge operator C in a supersymmetric framework

We argue that supersymmetric transformation could be applied across the heterojunction formed by joining of two mixed semiconductors. A general framework is described by specifying the structure of ladder operators at the junction for making quantitative estimation of physical quantities. For a particular heterojunction device, we show that an exponential grading inside a nanoscale doped layer is amenable to exact analytical treatment for a class of potentials distorted by the junctions through the solutions of transformed Morse-type potentials. © 2010 Elsevier B.V. All rights reserved.

Physics Letters, Section A: General, Atomic and Solid State Physics

Supersymmetry across nanoscale heterojunction

We consider the specific models of Zhu-Kroemer and BenDaniel-Duke in a sech(2)-mass background and point out interesting correspondences with the stationary 1-soliton and 2-soliton solutions of the KdV equation in a supersymmetric framework.

Journal of Physics A: Mathematical and Theoretical

Position-dependent mass models and their nonlinear characterization

A new quantum model with rational functions for the potential and effective mass is proposed in a stretchable region outside which both are constant. Starting from a generalized effective mass kinetic energy operator the matching and boundary conditions for the envelope wavefunctions are derived. It is shown that in a mapping to an auxiliary constant-mass Schrödinger picture one obtains one-period 'associated Lamé' well bounded by two δ-wells or δ-barriers depending on the values of the ordering parameter β. The results for bound states of this new solvable model are provided for a wide variation of the parameters. © 2006 IOP Publishing Ltd.

Journal of Physics A: Mathematical and General

We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of -symmetric Hamiltonians. The method is applied to the Hermitian analogue of the -symmetric cubic anharmonic oscillator. A new example is provided by a Hamiltonian (approximately) equivalent to a -symmetric extension of the one-parameter trigonometric Pöschl-Teller potential. © 2006 IOP Publishing Ltd.

Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework

By using the point canonical transformation approach in a manner distinct from previous ones, we generate some new exactly solvable or quasi-exactly solvable potentials for the one-dimensional Schrödinger equation with a position-dependent effective mass. In the latter case, SUSYQM techniques provide us with some additional new potentials. © EDP Sciences.

Journal	Modern Physics Letters A
Publisher	-
ISSN	0217-7323
Open Access	Yes