Displaced Harmonic Oscillator V ∼ min [(x + d)2, (x − d)2] as a Benchmark Double-Well Quantum Model

0563835 - ÚJF 2023 RIV CH eng J - Journal Article
Znojil, Miloslav
Displaced Harmonic Oscillator V ∼ min [(x + d)2, (x − d)2] as a Benchmark Double-Well Quantum Model.
Quantum Reports. Roč. 4, č. 3 (2022), s. 309-323. E-ISSN 2624-960X
Institutional support: RVO:61389005
Keywords : displaced harmonic oscillators * double-well–single-well transition * matching-method solutions * quasi-exact and non-polynomial exact bound states
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Method of publishing: Open access
https://doi.org/10.3390/quantum4030022

For the displaced harmonic double-well oscillator, the existence of exact polynomial bound states at certain displacements (Formula presented.) is revealed. The N-plets of these quasi-exactly solvable (QES) states are constructed in closed form. For non-QES states, the Schrödinger 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.
Permanent Link: https://hdl.handle.net/11104/0335628