Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials

Christiansen, H. R.; Cunha, M. S.

doi:10.1063/1.4840615

Title: Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials

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Abstract

We analytically solve the position-dependent mass (PDM) 1D Schrödinger equation for a new class of hyperbolic potentials V{sub q}{sup p}(x)=−V{sub 0}(sinh{sup p}x/cosh{sup q}x), p=−2,0,⋯q [see C. A. Downing, J. Math. Phys. 54, 072101 (2013)] among several hyperbolic single- and double-wells. For a solitonic mass distribution, m(x)=m{sub 0} sech{sup 2}(x), we obtain exact analytic solutions to the resulting differential equations. For several members of the class, the quantum mechanical problems map into confluent Heun differential equations. The PDM Poschl-Teller potential is considered and exactly solved as a particular case.

Authors:

Christiansen, H. R. ^[1]; Cunha, M. S. ^[2]

Physics Department, State University Vale do Acaraú, Av. da Universidade 850, 62040-370 Sobral-CE (Brazil)
Grupo de Física Teórica, State University of Ceara (UECE), Av. Paranjana 1700, 60740-903 Fortaleza-CE (Brazil)

Publication Date:: Sun Dec 15 00:00:00 EST 2013

OSTI Identifier:: 22217738

Resource Type:: Journal Article

Journal Name:: Journal of Mathematical Physics

Additional Journal Information:: Journal Volume: 54; Journal Issue: 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; EXACT SOLUTIONS; MASS DISTRIBUTION; POTENTIALS; QUANTUM MECHANICS; SCHROEDINGER EQUATION

Citation Formats


                    Christiansen, H. R., Grupo de Física Teórica, State University of Ceara, and Cunha, M. S. Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials.  United States: N. p., 2013. 
        Web.  doi:10.1063/1.4840615.

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                    Christiansen, H. R., Grupo de Física Teórica, State University of Ceara, & Cunha, M. S. Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials.  United States.  https://doi.org/10.1063/1.4840615

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                    Christiansen, H. R., Grupo de Física Teórica, State University of Ceara, and Cunha, M. S. 2013.  
        "Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials".  United States.  https://doi.org/10.1063/1.4840615.

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@article{osti_22217738,

  title        = {Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials},

  author       = {Christiansen, H. R. and Grupo de Física Teórica, State University of Ceara and Cunha, M. S.},

  abstractNote = {We analytically solve the position-dependent mass (PDM) 1D Schrödinger equation for a new class of hyperbolic potentials V{sub q}{sup p}(x)=−V{sub 0}(sinh{sup p}x/cosh{sup q}x), p=−2,0,⋯q [see C. A. Downing, J. Math. Phys. 54, 072101 (2013)] among several hyperbolic single- and double-wells. For a solitonic mass distribution, m(x)=m{sub 0} sech{sup 2}(x), we obtain exact analytic solutions to the resulting differential equations. For several members of the class, the quantum mechanical problems map into confluent Heun differential equations. The PDM Poschl-Teller potential is considered and exactly solved as a particular case.},

  doi          = {10.1063/1.4840615},

  url          = {https://www.osti.gov/biblio/22217738},
  journal      = {Journal of Mathematical Physics},

  issn         = {0022-2488},

  number       = 12,

  volume       = 54,

  place        = {United States},

  year         = {Sun Dec 15 00:00:00 EST 2013},

  month        = {Sun Dec 15 00:00:00 EST 2013}

}

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