A unified treatment of exactly solvable and quasi-exactly solvable quantum potentials

Abstract

By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable quantum potentials. We obtain, in this way, two new classes of quasi-exactly solvable systems one of which is of periodic type while the other hyperbolic.

arXiv commentLaTeX2e, 8 pages, To appear in J. Phys. A:Mathematical and general(letters)

References in corpus (5)

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• Associated LamÉ Equation, Periodic Potentials and sl(2,R)
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• Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
• New approach to (quasi)-exactly solvable Schrodinger equations with a position-dependent effective mass
• Extending the class of solvable potentials: III. The hyperbolic single wave
• Explicit Solutions for N-Dimensional Schrodinger Equations with Position-Dependent Mass
• Specific heats of quantum double-well systems
• L2 series solutions of the Dirac equation for power-law potentials at rest mass energy
• Equivalence of two alternative approaches to Schrodinger equations
• A class of singular logarithmic potentials in a box with variety of skin thickness and wall interaction
• Dynamical properties of an exactly solvable coupled quantum double-well system: The evolution speed and entanglement
• Integral relations and new solutions to the double-confluent Heun equation