Geodesic
Additional constraints on quasi-exactly solvable systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 150 (2007) no. 2, pp. 237-248

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We consider constraints on two-dimensional quantum mechanical systems in domains with boundaries. The constraints result from the Hermiticity requirement for the corresponding Hamiltonians. We construct new two-dimensional families of formally exactly solvable systems. Taking the mentioned constraints into account, we show that the systems are in fact quasi-exactly solvable at best. Nevertheless, in the context of pseudo-Hermitian Hamiltonians, some of the constructed families are exactly solvable.
Keywords: quasi-exactly solvable system, pseudo-Hermitian Hamiltonian. 
@article{TMF_2007_150_2_a4,
     author = {S. M. Klishevich},
     title = {Additional constraints on quasi-exactly solvable systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {237--248},
     publisher = {mathdoc},
     volume = {150},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_150_2_a4/}
}
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S. M. Klishevich. Additional constraints on quasi-exactly solvable systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 150 (2007) no. 2, pp. 237-248. http://geodesic.mathdoc.fr/item/TMF_2007_150_2_a4/