Geodesic
Some properties of the~shape-invariant two-dimensional Scarf~II model
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 99-108

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We consider the two-dimensional Scarf II quantum model in the framework of supersymmetric quantum mechanics. We systematize results previously obtained for this integrable system and derive some new properties. In particular, we show that the model is exactly or quasi-exactly solvable in different regions of the system parameter values. We find a degeneracy of the spectrum for some specific parameter values. We calculate the action of symmetry operators of the fourth order in momenta for arbitrary wave functions obtained using the double shape invariance.
Keywords: supersymmetry, shape invariance, integrable model, exact solvability, intertwining relation. 
@article{TMF_2015_185_1_a8,
     author = {M. V. Ioffe and E. V. Kolevatova and D. N. Nishnianidze},
     title = {Some properties of the~shape-invariant two-dimensional {Scarf~II} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {99--108},
     publisher = {mathdoc},
     volume = {185},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a8/}
}
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M. V. Ioffe; E. V. Kolevatova; D. N. Nishnianidze. Some properties of the~shape-invariant two-dimensional Scarf~II model. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 1, pp. 99-108. http://geodesic.mathdoc.fr/item/TMF_2015_185_1_a8/