New exact solutions for polynomial oscillators in large dimension

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F03%3A00101865" target="_blank" >RIV/61389005:_____/03:00101865 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
New exact solutions for polynomial oscillators in large dimension
Original language description
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 itsbound 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
Czech name
Nová přesná řešení pro polynomiální oscilátory při velkých dimensích
Czech description
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.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
—

Project
<a href="/en/project/IAA1048302" target="_blank" >IAA1048302: Quantum teory and pseudo-Hermitian Hamiltonians</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2003
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)