0101865 - UJF-V 20043048 RIV GB eng J - Journal Article
Znojil, Miloslav - Yanovich, D. - Gerdt, VP.
New exact solutions for polynomial oscillators in large dimension.
[Nová přesná řešení pro polynomiální oscilátory při velkých dimensích.]
Journal of Physics. A - Mathematical and General Physics. Roč. 36, č. 23 (2003), s. 6531-6549. ISSN 0305-4470
R&D Projects: GA AV ČR IAA1048302
Institutional research plan: CEZ:AV0Z1048901
Keywords : symmetric quantum-mechanics * large-N expansion * potentials
Subject RIV: BE - Theoretical Physics
Impact factor: 1.357, year: 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

V D-měrném prostoru s hodně velkým D je v nultém řádu vyřešen problém tzv. kvazi-exaktních vázaných stavů v polynomiálních potenciálech s 2q vazbovými konstantami pro všechna q < 6.
Permanent Link: http://hdl.handle.net/11104/0009252