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

Journal Article · Sun Dec 15 00:00:00 EST 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4840615· OSTI ID:22217738

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

---

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

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.

• OSTI ID: 22217738
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

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