Factorization method and Darboux transformation for multidimensional Hamiltonians
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 2, pp. 183-198
A. A. Andrianov; N. V. Borisov; M. V. Ioffe. Factorization method and Darboux transformation for multidimensional Hamiltonians. Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 2, pp. 183-198. http://geodesic.mathdoc.fr/item/TMF_1984_61_2_a2/
@article{TMF_1984_61_2_a2,
     author = {A. A. Andrianov and N. V. Borisov and M. V. Ioffe},
     title = {Factorization method and {Darboux} transformation for multidimensional {Hamiltonians}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {183--198},
     year = {1984},
     volume = {61},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_61_2_a2/}
}
TY  - JOUR
AU  - A. A. Andrianov
AU  - N. V. Borisov
AU  - M. V. Ioffe
TI  - Factorization method and Darboux transformation for multidimensional Hamiltonians
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1984
SP  - 183
EP  - 198
VL  - 61
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1984_61_2_a2/
LA  - ru
ID  - TMF_1984_61_2_a2
ER  - 
%0 Journal Article
%A A. A. Andrianov
%A N. V. Borisov
%A M. V. Ioffe
%T Factorization method and Darboux transformation for multidimensional Hamiltonians
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1984
%P 183-198
%V 61
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1984_61_2_a2/
%G ru
%F TMF_1984_61_2_a2

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

A multidimensional generalization of the factorization and Darboux transformation which makes it possible to find connections between the spectra and eigenfunctions of quantum Hamiltonians is investigated. Multidimensional Hamiltonians whose spectra differ by one discrete level are constructed.

[1] Schrödinger E., Proc. Roy. Irish Acad., 46A:2 (1940), 9–16 | MR

[2] Schrödinger E., Proc. Roy. Irish Acad., 46A:14 (1941), 183–206 | MR | Zbl

[3] Infeld L., Hull T. E., Rev. Mod. Phys., 23:1 (1951), 21–68 | DOI | MR | Zbl

[4] Darboux G., Compt. Rend., 94 (1882), 1456–1459

[5] Crum M. M., Quart. J. Math. Oxford, 6:2 (1955), 121–128 | DOI | MR

[6] Faddeev L. D., UMN, 14:4 (1959), 57–119 | MR

[7] Matveev V. B., Lett. Math. Phys., 3 (1979), 213–216 | DOI | MR | Zbl

[8] Matveev V. B., Lett. Math. Phys., 3 (1979), 217–219 | DOI | MR

[9] Matveev V. B., Salle M. A., Lett. Math. Phys., 3 (1979), 425–429 | DOI | MR | Zbl

[10] Andrianov A. A., Borisov N. V., Ioffe M. V., Vsesoyuznaya konferentsiya po teorii sistem neskolkikh chastits s silnym vzaimodeistviem, Tezisy dokladov, LGU, L., 1983, 69–70

[11] Andrianov A. A., Borisov N. V., Ioffe M. V., Pisma v ZhETF, 39:2 (1984), 78–81 | MR

[12] Carmona R., Commun. Math. Phys., 62:2 (1978), 97–106 | DOI | MR | Zbl

[13] Landau L. D., Lifshits E. M., Kvantovaya mekhanika. Nerelyativistskaya teoriya, 4-e izd., Nauka, M., 1974, 752 pp. | MR

[14] Gilkey P. B., The index theorem and the heat equation, Publish or Perish, Inc., Boston, 1974, 125 pp. | MR | Zbl

[15] Andrianov A. A., Borisov N. V., Ioffe M. V., Eides M. I., TMF, 61:1 (1984), 17–28 | MR