Dirac equation, hydrogen atom spectrum and the Lamb shift in dynamical non-commutative spaces

• Published in: Pramāṇa Vol. 88; no. 5; pp. 1 - 5
• Main Authors: ALAVI, S A, REZAEI, N
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.05.2017; Springer Nature B.V
• Subjects: Astronomy; Astrophysics and Astroparticles; Dirac equation; Energy measurement; Observations and Techniques; Physics; Physics and Astronomy; Lamb shift; 11.15.−q; Dirac equation; 11.25.Sq; hydrogen atom; dynamical non-commutative spaces; 11.30.Er
• ISSN: 0304-4289; 0973-7111
• DOI: 10.1007/s12043-017-1381-4

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 2 P 1/2 , 2 S 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 2 P 1/2 and 2 S 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 2 S 1/2 level receives no correction.