About: New exact solutions for polynomial oscillators in large dimensions.

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About: New exact solutions for polynomial oscillators in large dimensions. Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (en)
Title	New exact solutions for polynomial oscillators in large dimensions. New exact solutions for polynomial oscillators in large dimensions. (en)
skos:prefLabel	New exact solutions for polynomial oscillators in large dimensions. New exact solutions for polynomial oscillators in large dimensions. (en)
skos:notation	RIV/61389005:_____/03:49033079!RIV/2004/AV0/A49004/N
http://linked.open.../vavai/riv/strany	6531;6549
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(KSK1010104)
http://linked.open...iv/cisloPeriodika	23
http://linked.open...vai/riv/dodaniDat	2004
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	617842
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/03:49033079
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	exact solution; large-N limit; anharmonic-oscillators (en)
http://linked.open.../riv/klicoveSlovo	large-N limit exact solution anharmonic-oscillators
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[7E0B582B0E29]
http://linked.open...i/riv/nazevZdroje	JOURNAL OF PHYSICS. A-MATHEMATICAL AND GENERAL
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...ocetUcastnikuAkce	0 (xsd:int)
http://linked.open...nichUcastnikuAkce	0 (xsd:int)
http://linked.open...vavai/riv/projekt	Condensed matter physics and materials science
http://linked.open...UplatneniVysledku	2003
http://linked.open...v/svazekPeriodika	36
http://linked.open...iv/tvurceVysledku	Znojil, Miloslav Gerdt, V. P. Yanovich, D.
issn	0305-4470
number of pages	19 (xsd:int)

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