Abstract.
In this work we study and exactly solve the Dirac oscillator interacting with three different topological defects, namely the cosmic string spacetime (\(\Lambda_{\mp}\)), the magnetic cosmic string spacetime (\( \Theta_{\mp}\)) and the cosmic dislocation spacetime (\( \Pi_{\mp}\)). Moreover, we show that the radial part of this problem possesses an SU(1, 1) symmetry. Then, we obtain the wave functions and their respective energy spectrum by means of the Schrödinger factorization. Finally, we compute the radial coherent states and their time evolution in a general form for each topological defect.
Similar content being viewed by others
References
E. Copeland, D. Haws, S. Holbraad, R. Rivers, Nucl. Phys. B 319, 687 (1989)
A. Vilenkin, E.P.S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, Cambridge, 2000)
A.C. Davis, R. Brandenberger, Formation and Interaction of Topological Defects, in NATO Advanced Study of Institute, Series B: Physics, Vol. 349 (Plenum, New York, 1995)
D. Ito, K. Mori, E. Carrieri, Nuovo Cimento A 51, 1119 (1967)
P.A. Cook, Lett. Nuovo Cimento 1, 419 (1971)
M. Moshinsky, A. Szczepaniak, J. Phys. A 22, L817 (1989)
C. Quesne, M. Moshinsky, J. Phys. A 23, 2263 (1990)
J. Carvalho, C. Furtado, F. Moraes, Phys. Rev. A 84, 032109 (2011)
K. Bakke, Eur. Phys. J. Plus 127, 82 (2012)
K. Bakke, C. Furtado, Ann. Phys. (NY) 336, 489 (2013)
K. Bakke, Gen. Relativ. Gravit. 45, 1847 (2013)
F.M. Andrade, E.O. Silva, Eur. Phys. J. C 74, 3187 (2014)
O. Yeşiltaş, Eur. Phys. J. Plus 130, 128 (2015)
M. Salazar-Ramírez, D. Ojeda-Guillén, R.D. Mota, Ann. Phys. 372, 283 (2016)
J. Carvalho, A.M. de M. Carvalho, E. Cavalcante, C. Furtado, Eur. Phys. J. C 76, 365 (2016)
J.A. Neto, M.J. Bueno, C. Furtado, Ann. Phys. 373, 273 (2016)
J.A. Neto, J.R. de S. Oliveira, C. Furtado, S. Sergeenkov, Eur. Phys. J. Plus 133, 185 (2018)
L. Infeld, Phys. Rev. 59, 737 (1941)
L. Infeld, T.E. Hull, Rev. Mod. Phys. 23, 21 (1951)
A. Andrianov, N. Borisov, M. Ioffe, Phys. Lett. A 105, 19 (1984)
V. Spiridonov, L. Vinet, A. Zhedanov, Lett. Math. Phys. 29, 63 (1993)
M. Salazar-Ramírez, D. Martínez, R.D. Mota, V.D. Granados, EPL 95, 60002 (2011)
M. Salazar-Ramírez, D. Ojeda-Guillén, R.D. Mota, V.D. Granados, Eur. Phys. J. Plus 132, 39 (2017)
E. Schrödinger, Naturwissenschaften 14, 664 (1926)
R.J. Glauber, Phys. Rev. 130, 2529 (1963)
J.R. Klauder, Ann. Phys. 11, 123 (1960)
J.R. Klauder, J. Math. Phys. 4, 1055 (1963)
E.C.G. Sudarshan, Phys. Rev. Lett. 10, 227 (1963)
N.N. Lebedev, Special Functions and their Applications (Dover Publications, New York, 1972)
A.M. Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986)
C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics (Wiley-VCH, Berlin, 1977)
Y. Gur, A. Mann, Phys. At. Nucl. 68, 1700 (2005)
C.C. Gerry, J. Kiefer, Phys. Rev. A 37, 665 (1988)
M. Salazar-Ramírez, D. Ojeda-Guillén, R.D. Mota, J. Math. Phys. 57, 021704 (2016)
D.V. Gal'tsov, P.S. Letelier, Phys. Rev. D 47, 4273 (1993)
D. Ojeda-Guillén, R.D. Mota, V.D. Granados, J. Math. Phys. 57, 062104 (2016)
E. Choreño, D. Ojeda-Guillén, M. Salazar-Ramírez, V.D. Granados, Ann. Phys. 387, 121 (2017)
D. Loss, D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998)
H. Jeong, M.S. Kim, Phys. Rev. A 65, 042305 (2002)
T.C. Ralph, A. Gilchrist, G.J. Milburn, W.J. Munro, S. Glancy, Phys. Rev. A 68, 042319 (2003)
A. Vourdas, Phys Rev. A 41, 1653 (1990)
B.G. Adams, Algebraic Approach to Simple Quantum Systems (Springer, Berlin, 1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Salazar-Ramírez, M., Ojeda-Guillén, D., Morales-González, A. et al. Algebraic solution and coherent states for the Dirac oscillator interacting with a topological defect. Eur. Phys. J. Plus 134, 8 (2019). https://doi.org/10.1140/epjp/i2019-12381-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2019-12381-0