About: New exact solutions for polynomial oscillators in large dimension

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (cs) 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 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 (en)
Title	Nová přesná řešení pro polynomiální oscilátory při velkých dimensích (cs) New exact solutions for polynomial oscillators in large dimension New exact solutions for polynomial oscillators in large dimension (en)
skos:prefLabel	Nová přesná řešení pro polynomiální oscilátory při velkých dimensích (cs) New exact solutions for polynomial oscillators in large dimension New exact solutions for polynomial oscillators in large dimension (en)
skos:notation	RIV/61389005:_____/03:00101865!RIV/2005/AV0/A49005/N
http://linked.open.../vavai/riv/strany	6531;6549
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA1048302), Z(AV0Z1048901)
http://linked.open...iv/cisloPeriodika	23
http://linked.open...vai/riv/dodaniDat	2005
http://linked.open...aciTvurceVysledku	Znojil, Miloslav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav jaderné fyziky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	617841
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/03:00101865
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	symmetric quantum-mechanics;large-N expansion;potentials (en)
http://linked.open.../riv/klicoveSlovo	potentials large-N expansion symmetric quantum-mechanics
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[837E610A03EC]
http://linked.open...i/riv/nazevZdroje	Journal of Physics
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Quantum teory and pseudo-Hermitian Hamiltonians
http://linked.open...UplatneniVysledku	2003
http://linked.open...v/svazekPeriodika	36
http://linked.open...iv/tvurceVysledku	Znojil, Miroslav Gerdt, V. P. Yanovich, D.
http://linked.open...n/vavai/riv/zamer	Theoretical and experimental investigation of atomic nuclei and exploitation of nuclear methods in interdisciplinary research
issn	0305-4470
number of pages	19 (xsd:int)

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