Quasi-exactly solvable systems and orthogonal polynomials. (English) Zbl 0897.33014
This paper obtains a quasi-exactly solution to the Schrödinger equation. Its mathematical approach is based on a correspondence between quasi-exactly solvable models in quantum mechanics and sets of orthogonal polynomials. The quantum-mechanical wave function is the orthogonal polynomial in the energy. The condition of quasi-exact solvability is reflected in the vanishing of the norm of all polynomials. The zeros of the critical polynomial are the quasi-exact energy eigenvalues of the quantum mechanical systems.
Reviewer: Y.Kobayashi (Tottori)
MSC:
33C50 | Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
82B23 | Exactly solvable models; Bethe ansatz |
References:
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[2] | DOI: 10.1007/BF01466727 · Zbl 0683.35063 · doi:10.1007/BF01466727 |
[3] | DOI: 10.1142/S0217751X90000374 · Zbl 0709.58048 · doi:10.1142/S0217751X90000374 |
[4] | DOI: 10.1090/conm/160/01576 · doi:10.1090/conm/160/01576 |
[5] | DOI: 10.1090/conm/160/01570 · doi:10.1090/conm/160/01570 |
[6] | DOI: 10.1090/conm/160/01570 · doi:10.1090/conm/160/01570 |
[7] | DOI: 10.1063/1.530777 · Zbl 0806.40001 · doi:10.1063/1.530777 |
[8] | DOI: 10.1063/1.527635 · Zbl 0614.33025 · doi:10.1063/1.527635 |
[9] | DOI: 10.1063/1.531016 · Zbl 0843.45002 · doi:10.1063/1.531016 |
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