Geodesic
Algebraic approach to the solution of a one-dimensional model of $N$ interacting particles
Teoretičeskaâ i matematičeskaâ fizika, Tome 6 (1971) no. 3, pp. 364-391 
A. M. Perelomov. Algebraic approach to the solution of a one-dimensional model of $N$ interacting particles. Teoretičeskaâ i matematičeskaâ fizika, Tome 6 (1971) no. 3, pp. 364-391. http://geodesic.mathdoc.fr/item/TMF_1971_6_3_a6/
@article{TMF_1971_6_3_a6,
     author = {A. M. Perelomov},
     title = {Algebraic approach to~the~solution of~a~one-dimensional model of~$N$ interacting particles},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {364--391},
     year = {1971},
     volume = {6},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_6_3_a6/}
}
TY  - JOUR
AU  - A. M. Perelomov
TI  - Algebraic approach to the solution of a one-dimensional model of $N$ interacting particles
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1971
SP  - 364
EP  - 391
VL  - 6
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1971_6_3_a6/
LA  - ru
ID  - TMF_1971_6_3_a6
ER  - 
%0 Journal Article
%A A. M. Perelomov
%T Algebraic approach to the solution of a one-dimensional model of $N$ interacting particles
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1971
%P 364-391
%V 6
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1971_6_3_a6/
%G ru
%F TMF_1971_6_3_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

An algebraic apparatus based on increasing $B_p^+$ and decreasing $B_{p}$ operators $(p=2,3,\ldots,N)$ is developed to solve the one-dimensional model of N interacting particles studied by Calogero [J. Math. Phys., 10, 2191, 2197 (1969)]. The determination of the wave functions of the Schrödinger equation is then reduced to the operation of differentiation. Explicit expressions are obtained for the operators $B_{p}$ and $B_p^+$ for $p=2,3,$ and 4. All the wave functions for the case of four particles can be found by means of these expressions. For an arbitrary number of particles this then yields an expression for two new series of wave functions that depend on three quantum numbers. The operators of higher order can be found by the same method

[1] F. A. Berezin, G. P. Pokhil, V. M. Finkelberg, Vestnik MGU, 1964, no. 1, 21 | MR

[2] J. B. McGuire, J. Math. Phys., 5 (1964), 622 | DOI | MR | Zbl

[3] C. N. Yang, Phys. Rev. Lett., 19 (1967), 1312 ; Phys. Rev., 168 (1968), 1920 | DOI | MR | Zbl | DOI

[4] F. Calogero, J. Math. Phys., 10 (1969), 2191 | DOI | MR

[5] F. Calogero, J. Math. Phys., 10 (1969), 2197 | DOI | MR

[6] F. Calogero, Preprint, Nota Interna n. 267, Institute di Fisica “G. Marconi”, 1970 ; J. Math. Phys., 12 (1971) | Zbl | DOI | MR

[7] C. Marchioro, J. Math. Phys., 11 (1970), 2193 | DOI

[8] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, 1963 | MR

[9] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, v. 2, IL, 1966 | MR

[10] V. Bargmann, Ann. Math., 48 (1947), 568 | DOI | MR | Zbl

[11] A. M. Perelomov, V. S. Popov, I. A. Malkin, YaF, 2 (1965), 533 | MR

[12] Yu. M. Demkov, ZhETF, 44 (1963), 2007 | MR | Zbl

[13] P. Vinternits, Ya. A. Smorodinskii, M. Uglirzh, I. Frish, YaF, 4 (1966), 625