New exact solutions for polynomial oscillators in large dimensions

0185760 - UJF-V 20033079 RIV GB eng J - Článek v odborném periodiku
Znojil, Miloslav - Yanovich, D. - Gerdt, VP.
New exact solutions for polynomial oscillators in large dimensions.
Journal of Physics. A - Mathematical and General Physics. Roč. 36, č. 23 (2003), s. 6531-6549. ISSN 0305-4470
Grant CEP: GA AV ČR KSK1010104
Klíčová slova: exact solution * large-N limit * anharmonic-oscillators
Kód oboru RIV: BE - Teoretická fyzika
Impakt faktor: 1.357, rok: 2003

A new type of exact solvability is reported. The Schrodinger equation is considered in a very large spatial dimension D much greater than 1 and its central polynomial potential is allowed to depend on 'many' (= 2q) coupling constants. In a search for its bound states possessing an exact and elementary wavefunction (proportional to a harmonic-oscillator-like polynomial of a freely varying, i.e., not just small, degree N), the 'solvability conditions' are known to form a complicated nonlinear set which requires a purely numerical treatment at a generic choice of D, q and N. Assuming that D is large we discovered and demonstrate that this problem may be completely factorized and acquires an amazingly simple exact solution at all N and up to q = 5 at least.
Trvalý link: http://hdl.handle.net/11104/0082136