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Statements

Subject Item
n2:RIV%2F61389005%3A_____%2F03%3A00101865%21RIV%2F2005%2FAV0%2FA49005%2FN
rdf:type
skos:Concept n13:Vysledek
dcterms: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. 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
dcterms:title
Nová přesná řešení pro polynomiální oscilátory při velkých dimensích New exact solutions for polynomial oscillators in large dimension New exact solutions for polynomial oscillators in large dimension
skos:prefLabel
New exact solutions for polynomial oscillators in large dimension New exact solutions for polynomial oscillators in large dimension Nová přesná řešení pro polynomiální oscilátory při velkých dimensích
skos:notation
RIV/61389005:_____/03:00101865!RIV/2005/AV0/A49005/N
n4:strany
6531;6549
n4:aktivita
n7:Z n7:P
n4:aktivity
P(IAA1048302), Z(AV0Z1048901)
n4:cisloPeriodika
23
n4:dodaniDat
n5:2005
n4:domaciTvurceVysledku
n18:6594972
n4:druhVysledku
n11:J
n4:duvernostUdaju
n8:S
n4:entitaPredkladatele
n17:predkladatel
n4:idSjednocenehoVysledku
617841
n4:idVysledku
RIV/61389005:_____/03:00101865
n4:jazykVysledku
n15:eng
n4:klicovaSlova
symmetric quantum-mechanics;large-N expansion;potentials
n4:klicoveSlovo
n14:symmetric%20quantum-mechanics n14:large-N%20expansion n14:potentials
n4:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n4:kontrolniKodProRIV
[837E610A03EC]
n4:nazevZdroje
Journal of Physics
n4:obor
n16:BE
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
3
n4:projekt
n12:IAA1048302
n4:rokUplatneniVysledku
n5:2003
n4:svazekPeriodika
36
n4:tvurceVysledku
Znojil, Miroslav Yanovich, D. Gerdt, V. P.
n4:zamer
n10:AV0Z1048901
s:issn
0305-4470
s:numberOfPages
19