zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Exact operator solution of the Calogero-Sutherland model. (English) Zbl 0859.35103
Summary: The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived. The creation operators that enter in this formula of Rodrigues-type for the Jack polynomials involve Dunkl operators.

MSC:
35Q40PDEs in connection with quantum mechanics
82B23Exactly solvable models; Bethe ansatz
33E15Other wave functions
References:
[1]Calogero, F.: Solution of a three-body problem in one dimension. J. Math. Phys.10, 2191–2196 (1969) · doi:10.1063/1.1664820
[2]Sutherland, B.: Quantum many-body problem in one dimension, I, II. J. Math. Phys.12, 246–250 (1971) · doi:10.1063/1.1665584
[3]Sutherland, B.: An introduction to the Bethe ansatz. Exactly Solvable Problems in Condensed Matter and Relativistic Field Theory, B. S. Shastry, S. S. Jha, V. Singh (eds.) Berlin, Heidelberg, New York: Springer 1985, pp. 1–95
[4]Haldane, D.: Physics of the ideal fermion gas: Spinons and quantum symmetries of the integrable Haldane-Shastry spin chain. Correlation Effects in Low-Dimensional Electron Systems, A. Okiji, N. Kamakani (eds.) Berlin, Heidelberg, New-York: Springer 1995, pp. 3–20
[5]Ha, Z.N.C.: Exact dynamical correlation functions of the Calogero-Sutherland model and one dimensional fractional statistics in one dimension: View from an exactly solvable model. Nucl. Phys. B435, [FS], 604–636 (1995) · Zbl 1020.82538 · doi:10.1016/0550-3213(94)00537-O
[6]Lesage, F., Pasquier, V., Serban, D.: Dynamical correlation functions in the Calogero-Sutherland model. Nucl.Phys. B435, [FS], 585–603 (1995) · Zbl 1020.82539 · doi:10.1016/0550-3213(94)00453-L
[7]Forrester, P.J.: Selberg correlation integrals and the 1/r 2 quantum many-body system. Nucl. Phys. B388, 671–699 (1992); Integration formulas and exact calculations in the Calogero-Sutherland model. University of Melbourne preprint (1994) · doi:10.1016/0550-3213(92)90559-T
[8]Stanley, R.P.: Some combinatorial properties of Jack Symmetric functions. Adv. Math.77, 76–115 (1988) · Zbl 0743.05072 · doi:10.1016/0001-8708(89)90015-7
[9]Macdonald, I.G.: Symmetric Functions and Hall Polynomials. 2nd edition, Oxford: Clarendon Press, 1995
[10]Vilenkin, N.Ja., Klimyk, A.U.: Representation of Lie Groups and Special Functions. Dordrecht: Kluwer Academic Publishers, 1995
[11]Mimachi, K., Yamada, Y.: Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials. Commun. Math. Phys. (to appear)
[12]Awata, H., Matsuo, Y., Odake, S., Shiraishi, J.: Collective field theory, Calogero-Sutherland model and generalized matrix models. Phys. Lett B347, 49–55 (1995); Excited states of Calogero-Sutherland model and singular vectors of theW N algebra. Preprint (1995). · Zbl 0894.17027 · doi:10.1016/0370-2693(95)00055-P
[13]Bernard, D., Pasquier, V., Serban, D.: Spinons in conformal field theory. Nucl. Phys. B428, 612–628 (1994) · Zbl 1049.81535 · doi:10.1016/0550-3213(94)90366-2
[14]Bouwknegt, P., Ludwig, A.W.W., Schoutens, K.: Affine and Yangian symmetries in SU (2)1 conformal field theory. hep-th/9412199
[15]Dunkl, C.F.: Differential-difference operators associated to reflection groups. Trans. Am. Math. Soc.311, 167–183 (1989) · doi:10.1090/S0002-9947-1989-0951883-8
[16]Polychronakos, A.P.: Exchange operator formalism for integrable systems of particles. Phys. Rev. Lett.69, 703–705 (1992) · Zbl 0968.37521 · doi:10.1103/PhysRevLett.69.703
[17]Lapointe, L., Vinet, L.: In preparation
[18]Lapointe, L., Vinet, L.: A Rodrigues formula for the Jack polynomials and the Macdonald-Stanley conjecture. IMRN9, 419–424 (1995) · Zbl 0868.33009 · doi:10.1155/S1073792895000298
[19]Ruijsenaars, S.N.M.: Complete integrability of relativistic Calogero-Moser systems and elliptic function identities. Commun. Math. Phys.110, 191–213 (1987) · Zbl 0673.58024 · doi:10.1007/BF01207363