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Quasi-exactly solvable polynomial extensions of the quantum harmonic oscillator

2018
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Journal of Physics, Conference Series
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The (analytic) sextic oscillator is often considered as the prototype of quasi-exactly solvable (QES) Schrödinger equations, i.e., those Schrödinger equations for which at some ad hoc couplings a finite number of eigenstates can be found explicitly by algebraic means, while the remaining ones remain unknown. Recently, a (non-analytic) QES symmetrized quartic oscillator was introduced and shown to complete the list of (analytic) QES anharmonic oscillators, which does not contain any quartic one.

doi:10.1088/1742-6596/1071/1/012016
fatcat:mcv2uyzrbne27cua2cy2smgvty