ALGEBRAIC CONSTRUCTION OF THE EIGENSTATES FOR THE 2ND CONSERVED OPERATOR OF THE QUANTUM CALOGERO MODEL

Authors
UJINO H WADATI M
Citation
H. Ujino et M. Wadati, ALGEBRAIC CONSTRUCTION OF THE EIGENSTATES FOR THE 2ND CONSERVED OPERATOR OF THE QUANTUM CALOGERO MODEL, Journal of the Physical Society of Japan, 65(3), 1996, pp. 653-656
Citations number
20
Categorie Soggetti
Physics
Journal title
Journal of the Physical Society of Japan → ACNP
ISSN journal
00319015
Volume
65
Issue
3
Year of publication
1996
Pages
653 - 656
Database
ISI
SICI code
0031-9015(1996)65:3<653:ACOTEF>2.0.ZU;2-#
Abstract
An algebraic construction of the eigenstates for the quantum Calogero model is investigated. Extending the method of Lapointe and Vinet, we construct the eigenstates for the second conserved operator of the qua ntum Calogero model. All the eigenstates can be factorized into symmet ric polynomials which we call ''Hi-Jack symmetric polynomials'' and th e ground state wave function. The conjectured formula for the eigenval ue of the second conserved operator is confirmed. The Hi-Jack polynomi als are strong candidates for the orthogonal. basis of the quantum Cal ogero model.