Analytical solution to position dependent mass Schrödinger equation

Pankaj K. Jha; Hichem Eleuch; Yuri V. Rostovtsev

doi:10.1080/09500340.2011.562617

Analytical solution to position dependent mass Schrödinger equation

Pankaj K. Jha, Hichem Eleuch, Yuri V. Rostovtsev

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

Using a recently developed technique to solve the Schrödinger equation for constant mass, we have studied the regime in which the mass varies with position, i.e. the position-dependent mass Schrödinger equation (PDMSE). We obtained an analytical solution for the PDMSE and applied our approach to study a position dependent mass m(x) particle scattered by a potential ν(x). We have also studied the structural analogy between the PDMSE and the two-level atomic system interacting with a classical field.

Original language	English (US)
Pages (from-to)	652-656
Number of pages	5
Journal	Journal of Modern Optics
Volume	58
Issue number	8
DOIs	https://doi.org/10.1080/09500340.2011.562617
State	Published - May 10 2011
Externally published	Yes

Keywords

Position dependent mass
Riccati equation
Rotating wave approximation
Scattering
Two-level system

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics

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10.1080/09500340.2011.562617

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title = "Analytical solution to position dependent mass Schr{\"o}dinger equation",

abstract = "Using a recently developed technique to solve the Schr{\"o}dinger equation for constant mass, we have studied the regime in which the mass varies with position, i.e. the position-dependent mass Schr{\"o}dinger equation (PDMSE). We obtained an analytical solution for the PDMSE and applied our approach to study a position dependent mass m(x) particle scattered by a potential ν(x). We have also studied the structural analogy between the PDMSE and the two-level atomic system interacting with a classical field.",

keywords = "Position dependent mass, Riccati equation, Rotating wave approximation, Scattering, Two-level system",

author = "Jha, {Pankaj K.} and Hichem Eleuch and Rostovtsev, {Yuri V.}",

note = "Funding Information: We thank M.O. Scully, L.V. Keldysh, M.S. Zubairy, Chia-Ren Hu, S.A. Chin, G. Agnolet for useful discussions. We also gratefully acknowledge support from NSF Grant No. EEC-0540832 (MIRTHE ERC), the Office of Naval Research (Grant Nos. N00014-09-1-0888 and N0001408-1-0948), and the Robert A. Welch Foundation (Award No. A-1261) and partial support from the CRDF. P.K.J. also acknowledges the Robert A. Welch Foundation and HEEP Foundation for financial support. Y.V.R. gratefully acknowledges support from the UNT Research Initiation Grant and the summer fellowship UNT program.",

year = "2011",

month = may,

day = "10",

doi = "10.1080/09500340.2011.562617",

language = "English (US)",

volume = "58",

pages = "652--656",

journal = "Journal of Modern Optics",

issn = "0950-0340",

publisher = "Taylor and Francis Ltd.",

number = "8",

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TY - JOUR

T1 - Analytical solution to position dependent mass Schrödinger equation

AU - Jha, Pankaj K.

AU - Eleuch, Hichem

AU - Rostovtsev, Yuri V.

N1 - Funding Information: We thank M.O. Scully, L.V. Keldysh, M.S. Zubairy, Chia-Ren Hu, S.A. Chin, G. Agnolet for useful discussions. We also gratefully acknowledge support from NSF Grant No. EEC-0540832 (MIRTHE ERC), the Office of Naval Research (Grant Nos. N00014-09-1-0888 and N0001408-1-0948), and the Robert A. Welch Foundation (Award No. A-1261) and partial support from the CRDF. P.K.J. also acknowledges the Robert A. Welch Foundation and HEEP Foundation for financial support. Y.V.R. gratefully acknowledges support from the UNT Research Initiation Grant and the summer fellowship UNT program.

PY - 2011/5/10

Y1 - 2011/5/10

N2 - Using a recently developed technique to solve the Schrödinger equation for constant mass, we have studied the regime in which the mass varies with position, i.e. the position-dependent mass Schrödinger equation (PDMSE). We obtained an analytical solution for the PDMSE and applied our approach to study a position dependent mass m(x) particle scattered by a potential ν(x). We have also studied the structural analogy between the PDMSE and the two-level atomic system interacting with a classical field.

AB - Using a recently developed technique to solve the Schrödinger equation for constant mass, we have studied the regime in which the mass varies with position, i.e. the position-dependent mass Schrödinger equation (PDMSE). We obtained an analytical solution for the PDMSE and applied our approach to study a position dependent mass m(x) particle scattered by a potential ν(x). We have also studied the structural analogy between the PDMSE and the two-level atomic system interacting with a classical field.

KW - Position dependent mass

KW - Riccati equation

KW - Rotating wave approximation

KW - Scattering

KW - Two-level system

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SP - 652

EP - 656

JO - Journal of Modern Optics

JF - Journal of Modern Optics

IS - 8

ER -

Analytical solution to position dependent mass Schrödinger equation

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Keywords

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