Do Quasi-Exactly Solvable Systems Always Correspond to Orthogonal Polynomials?
Khare, Avinash ; Mandal, Bhabani Prasad
arXiv, 9709043 / Harvested from arXiv
Text on arXiv
We consider two quasi-exactly solvable problems in one dimension for which the Schr\"odinger equation can be converted to Heun's equation. We show that in neither case the Bender-Dunne polynomials form an orthogonal set. Using the anti-isopectral transformation we also discover a new quasi-exactly solvable problem and show that even in this case the polynomials do not form an orthogonal set.
Publié le : 1997-09-30
Classification:  Mathematical Physics,  High Energy Physics - Theory,  Quantum Physics 
@article{9709043,
     author = {Khare, Avinash and Mandal, Bhabani Prasad},
     title = {Do Quasi-Exactly Solvable Systems Always Correspond to Orthogonal
  Polynomials?},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9709043}
}

Khare, Avinash; Mandal, Bhabani Prasad. Do Quasi-Exactly Solvable Systems Always Correspond to Orthogonal
  Polynomials?. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9709043/