Abstract
We derive the relativistic Hamiltonian of hydrogen atom in dynamical non-commutative spaces (DNCS or τ-space). Using this Hamiltonian we calculate the energy shift of the ground state as well the 2P 1/2, 2S 1/2 levels. In all the cases, the energy shift depends on the dynamical non-commutative parameter τ. Using the accuracy of the energy measurement, we obtain an upper bound for τ. We also study the Lamb shift in DNCS. Both 2P 1/2 and 2S 1/2 levels receive corrections due to dynamical non-commutativity of space which is in contrast with the non-dynamical non-commutative spaces (NDNCS or 𝜃-space) in which the 2S 1/2 level receives no correction.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V O Rivelles, J. Phys. Conf. Ser. 287, 012012 (2011)
V Gáliková, S Kováčik and P Prešnajder, Acta Phys. Slov. 65, 153 (2015)
L Gouba, Int. J. Mod. Phys. A 31, 1630025 (2016)
M Gomes and V G Kupriyanov, Phys. Rev. D 79, 125011 (2009)
M Gomes, V G Kupriyanov and A J da Silva, J. Phys. A 43, 285301 (2010)
A Fring, L Gouba and F G Scholtz, J. Phys. A 43, 345401 (2010)
M Chaichian, M M Sheikh-Jabbari and A Tureanu, Phys. Rev. Lett. 86, 2716 (2001) Eur. Phys. J. C 36, 251 (2004)
T C Adorno, M C Baldiotti, M Chaichian, D M Gitman and A Tureanu, Phys. Lett. B 682, 235 (2009)
Y Jiang, J. Phys. A: Math. Gen. 38, 1157 (2005)
W Greiner, Relativistic quantum mechanics-wave equations (Springer, Berlin, 1990)
L Essen et al, Nature 229, 110 (1971)
S A Alavi and M Amiri Nasab, Gen. Relativ. Gravit. 49, 5 (2017) arXiv:1512.08236
S A Alavi, Phys. Scr. 78, 015005 (2008)
S A Alavi and S Nodeh, Phys. Scr. 90, 035301 (2015)
S A Alavi and S Abbaspour, J. Phys. A: Math. Theor. 47, 045303 (2014)
A Smailagic and E Spallucci, J. Phys. A 35, L363 (2002)
I Dadic, L Jonke and S Meljanac, Acta Phys. Slov. 55, 149 (2005)
Non-Hermitian Hamiltonians in quantum physics, Pramana – J. Phys. 73(2), 215–422 (2009) Pramana – J. Phys. 73(3), 417–622 (2009)
Pseudo-Hermitian Hamiltonians in quantum physics IX, Int. J. Theor. Phys. 50(4), 953–1333 (2011)
Quantum physics with non-Hermitian operators, J. Phys. A: Math. Theor. 45, 44 (2012)
14 th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics, Int. J. Theor. Phys. 54(11), 3867–4183 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
ALAVI, S.A., REZAEI, N. Dirac equation, hydrogen atom spectrum and the Lamb shift in dynamical non-commutative spaces. Pramana - J Phys 88, 77 (2017). https://doi.org/10.1007/s12043-017-1381-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12043-017-1381-4