Quasi Exactly Solvable Difference Equations

Abstract

Several explicit examples of quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known quasi exactly solvable systems, the harmonic oscillator (with/without the centrifugal potential) deformed by a sextic potential and the 1/sin^2x potential deformed by a cos2x potential. They have a finite number of exactly calculable eigenvalues and eigenfunctions.

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Cited by in corpus (12)

• Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
• Orthogonal Polynomials from Hermitian Matrices
• Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
• Discrete Quantum Mechanics
• Orthogonal Polynomials from Hermitian Matrices II
• Relativistic Solutions of Generalized-Dunkl Harmonic and Anharmonic Oscillators
• q-oscillator from the q-Hermite Polynomial
• Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism
• New Quasi Exactly Solvable Difference Equation
• Multi-Particle Quasi Exactly Solvable Difference Equations
• Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
• Exactly and quasi-exactly solvable `discrete' quantum mechanics