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arXiv · 0708.0702

Quasi Exactly Solvable Difference Equations

Ryu Sasaki
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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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Ryu Sasaki. 2007-10-11. Quasi Exactly Solvable Difference Equations. https://doi.org/10.1063/1.2818560

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