Geodesic
A new two-parameter family of exactly solvable Dirac Hamiltonians
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 2, pp. 243-251 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Using the Darboux transformation method, we construct a two-parameter family of exactly solvable Dirac Hamiltonians. We obtain intertwining relations between various members of this family. We study the spectral properties of these Hamiltonians and give explicit expressions for their eigenfunctions.
Mots-clés : Darboux transformation, Dirac equation
Keywords: supersymmetry. 
@article{TMF_2009_159_2_a4,
     author = {E. O. Pozdeeva},
     title = {A~new two-parameter family of exactly solvable {Dirac} {Hamiltonians}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {243--251},
     year = {2009},
     volume = {159},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_2_a4/}
}
TY  - JOUR
AU  - E. O. Pozdeeva
TI  - A new two-parameter family of exactly solvable Dirac Hamiltonians
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2009
SP  - 243
EP  - 251
VL  - 159
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2009_159_2_a4/
LA  - ru
ID  - TMF_2009_159_2_a4
ER  - 
%0 Journal Article
%A E. O. Pozdeeva
%T A new two-parameter family of exactly solvable Dirac Hamiltonians
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2009
%P 243-251
%V 159
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2009_159_2_a4/
%G ru
%F TMF_2009_159_2_a4
E. O. Pozdeeva. A new two-parameter family of exactly solvable Dirac Hamiltonians. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 2, pp. 243-251. http://geodesic.mathdoc.fr/item/TMF_2009_159_2_a4/

[1] G. Darboux, C. R. Acad. Sci. Paris, 94 (1882), 1456–1459 ; arXiv: physics/9908003 | Zbl

[2] G. Darboux, Leçons sur la théorie des surfaces, II, Gauthier-Villars, Paris, 1889 | MR | Zbl

[3] M. M. Crum, Quart. J. Math., 6 (1955), 121–127 | DOI | MR | Zbl

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

[5] V. B. Matveev, Lett. Math. Phys., 3:3 (1979), 217–222 | DOI | MR | Zbl

[6] M. A. Sall, TMF, 53:2 (1982), 227–237 | DOI | MR | Zbl

[7] V. B. Matveev, M. A. Salle, Darboux Transformations and Solitons, Springer Ser. Nonlinear Dynam., Springer, Berlin, 1991 | DOI | MR | Zbl

[8] S. G. Krein, DAN SSSR, 113:6 (1957), 970–973 | MR | Zbl

[9] F. Cooper, A. Khare, U. Sukhatme, Phys. Rep., 251:5–6 (1995), 267–385 | DOI | MR

[10] L. M. Nieto, H. C. Rosu, M. Santander, Modern Phys. Lett. A, 14 (1999), 35–41 | DOI | MR

[11] D. Chang, We-Fu Chang, Chinese J. Phys., 33:5 (1995), 493–504 | MR

[12] K. Klein, V. B. Matveev, A. O. Smirnov, TMF, 152:2 (2007), 304–320 | DOI | MR | Zbl

[13] E. O. Pozdeeva, Internat. J. Modern. Phys. A, 23:2 (2008), 247–258 | DOI | MR | Zbl

[14] E. O. Pozdeeva, J. Phys. A, 41:14 (2008), 145208 | DOI | MR | Zbl

[15] L. M. Nieto, A. A. Pecheritsin, B. F. Samsonov, Ann. Physics, 305:2 (2003), 151–189 | DOI | MR | Zbl

[16] L. D. Landau, E. M. Livshits, Teoreticheskaya fizika. T. 3. Kvantovaya mekhanika. Nerelyativistskaya teoriya, Nauka, M., 1974 | MR | MR | Zbl

[17] G. Pöschl, E. Teller, Z. Phys., 83:3–4 (1933), 143–151 | DOI | Zbl

[18] P. Gaillard, V. Matveev, Wronskian addition formula and its applications, Preprint, Max-Planck-Institut für Mathematik, Bonn, MPIM 02-31, 2002 | MR

[19] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatlit, M., 1971 | MR | MR | Zbl

[20] B. F. Samsonov, European J. Phys., 22:4 (2001), 305–313 | DOI | MR | Zbl

[21] B. F. Samsonov, A. A. Pecheritsin, E. O. Pozdeeva, M. L. Glasser, European J. Phys., 24:4 (2003), 435–441 | DOI | MR | Zbl

[22] V. G. Bagrov, A. A. Pecheritsin, E. O. Pozdeeva, B. F. Samsonov, Commun. Nonlinear Sci. Numer. Simul., 9:1 (2004), 13–23 | DOI | MR | Zbl