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Statements

Subject Item
n2:RIV%2F61389005%3A_____%2F03%3A49033079%21RIV%2F2004%2FAV0%2FA49004%2FN
rdf:type
skos:Concept n16:Vysledek
dcterms: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 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
New exact solutions for polynomial oscillators in large dimensions. New exact solutions for polynomial oscillators in large dimensions.
skos:prefLabel
New exact solutions for polynomial oscillators in large dimensions. New exact solutions for polynomial oscillators in large dimensions.
skos:notation
RIV/61389005:_____/03:49033079!RIV/2004/AV0/A49004/N
n4:strany
6531;6549
n4:aktivita
n6:P
n4:aktivity
P(KSK1010104)
n4:cisloPeriodika
23
n4:dodaniDat
n15:2004
n4:domaciTvurceVysledku
n13:6594972
n4:druhVysledku
n9:J
n4:duvernostUdaju
n11:S
n4:entitaPredkladatele
n10:predkladatel
n4:idSjednocenehoVysledku
617842
n4:idVysledku
RIV/61389005:_____/03:49033079
n4:jazykVysledku
n17:eng
n4:klicovaSlova
exact solution; large-N limit; anharmonic-oscillators
n4:klicoveSlovo
n7:exact%20solution n7:large-N%20limit n7:anharmonic-oscillators
n4:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n4:kontrolniKodProRIV
[7E0B582B0E29]
n4:nazevZdroje
JOURNAL OF PHYSICS. A-MATHEMATICAL AND GENERAL
n4:obor
n5:BE
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
3
n4:pocetUcastnikuAkce
0
n4:pocetZahranicnichUcastnikuAkce
0
n4:projekt
n14:KSK1010104
n4:rokUplatneniVysledku
n15:2003
n4:svazekPeriodika
36
n4:tvurceVysledku
Gerdt, V. P. Znojil, Miloslav Yanovich, D.
s:issn
0305-4470
s:numberOfPages
19