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

Abstract

We analytically solve the position-dependent mass (PDM) 1D Schrödinger equation for a new class of hyperbolic potentials $V_q^p(x)=-V_0\frac{{\sinh }^{p}x}{{\cosh }^{q}x},p=-2,0,\dots q$ [see C. A. Downing, J. Math. Phys. 54 072101 (2013)] among which several hyperbolic single- and double-wells. For a solitonic mass distribution, $m(x)=m_0{\text{sech}}^2(x)$, 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.

Some typos corrected. Some references updated. The acronym in the title expanded. 15 pages, 27 figures

References in corpus (3)

• Exact solution of Schrodinger equation for modified Kratzer's molecular potential with the position-dependent mass
• The Spin of Holographic Electrons at Nonzero Density and Temperature
• Kalb-Ramond excitations in a thick-brane scenario with dilaton

Cited by in corpus (8)

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• Energy eigenfunctions for position-dependent mass particles in a new class of molecular hamiltonians
• The kinetic Hamiltonian with position-dependent mass
• The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass
• Energy eigenstates of position-dependent mass particles in a spherical quantum dot
• Three-dimensional bound states of cylindrical quantum heterostructures with position-dependent mass carriers
• Physical Problems Admitting Heun-to-Hypergeometric Reduction
• Effective particles in a multishell nanostructure with hardcore