Displaced harmonic oscillator $V\sim \min \,[(x+d)^2,(x-d)^2]$ as a benchmark double-well quantum model
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Publication:6275267
DOI10.3390/QUANTUM4030022arXiv1607.01297WikidataQ114027137 ScholiaQ114027137MaRDI QIDQ6275267
Publication date: 5 July 2016
Abstract: For the displaced harmonic double-well oscillator the existence of exact polynomial bound states at certain displacements is revealed. The plets of these quasi-exactly solvable (QES) states are constructed in closed form. For non-QES states, Schr"{o}dinger equation can still be considered ``non-polynomially exactly solvable (NES) because the exact left and right parts of the wave function (proportional to confluent hypergeometric function) just have to be matched in the origin.
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