New implicitly solvable potential produced by second order shape invariance

Journal Article · Fri May 15 00:00:00 EDT 2015 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2015.03.020· OSTI ID:22451175

Cannata, F., E-mail: [e-mail] ^[1]; Ioffe, M.V., E-mail: [e-mail] ^[2]; Kolevatova, E.V., E-mail: [e-mail] ^[2]; Nishnianidze, D.N., E-mail: [e-mail] ^[3]; Saint Petersburg State University, 198504 Saint-Petersburg ^[4]

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1. INFN, Via Irnerio 46, 40126 Bologna (Italy)
2. Saint Petersburg State University, 198504 Saint-Petersburg (Russian Federation)
3. Akaki Tsereteli State University, 4600 Kutaisi, Georgia (United States)
4. (Russian Federation)

The procedure proposed recently by Bougie et al. (2010) to study the general form of shape invariant potentials in one-dimensional Supersymmetric Quantum Mechanics (SUSY QM) is generalized to the case of Higher Order SUSY QM with supercharges of second order in momentum. A new shape invariant potential is constructed by this method. It is singular at the origin, it grows at infinity, and its spectrum depends on the choice of connection conditions in the singular point. The corresponding Schrödinger equation is solved explicitly: the wave functions are constructed analytically, and the energy spectrum is defined implicitly via the transcendental equation which involves Confluent Hypergeometric functions. - Highlights: • New potential with 2nd order irreducible shape invariance was constructed. • The connection conditions at the singularity of potential were obtained. • The explicit expressions for all wave functions were derived. • The implicit equation for the energy spectrum was obtained.

• OSTI ID: 22451175
• Journal Information: Annals of Physics, Vol. 356; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ENERGY SPECTRA
HYPERGEOMETRIC FUNCTIONS
ONE-DIMENSIONAL CALCULATIONS
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SUPERSYMMETRY
WAVE FUNCTIONS