Transformed Dirac equation for the hydrogen atom, comparison with previous approaches in momentum space, and the anomalous Zeeman effect in momentum representation

2003 ◽  
Vol 96 (1) ◽  
pp. 42-55 ◽  
Author(s):  
Sambhu N. Datta
Keyword(s):  
Hydrogen Atom ◽  
Dirac Equation ◽  
Momentum Space ◽  
Zeeman Effect ◽  
Momentum Representation ◽  
Anomalous Zeeman Effect

Phenomenology of noncommutative phase space via the anomalous Zeeman effect in hydrogen atom

2014 ◽  
Vol 29 (31) ◽  
pp. 1450177 ◽  
Author(s):  
Willien O. Santos ◽  
Andre M. C. Souza
Keyword(s):  
Phase Space ◽  
Hydrogen Atom ◽  
Zeeman Effect ◽  
Nonrelativistic Limit ◽  
Noncommutative Phase Space ◽  
G Factor ◽  
First Order ◽  
Anomalous Zeeman Effect ◽  
Space Noncommutativity ◽  
First Order Perturbation

The Hamiltonian describing the anomalous Zeeman effect for the hydrogen atom on noncommutative (NC) phase space is studied using the nonrelativistic limit of the Dirac equation. To preserve gauge invariance, space noncommutativity must be dropped. By using first-order perturbation theory, the correction to the energy is calculated for the case of a weak external magnetic field. We also obtained the orbital and spin g-factors on the NC phase space. We show that the experimental value for the spin g-factor puts an upper bound on the magnitude of the momentum NC parameter of the order of [Formula: see text], 34 μ eV /c. On the other hand, the experimental value for the spin g-factor was used to establish a correction introduced by NC phase space to the presently accepted value of Planck's constant with an uncertainty of 2 part in 1035.

scholarly journals Resolution in the Case of the Hydrogen Atom of an Improved Dirac Equation

2020 ◽  
Vol 11 (07) ◽  
pp. 1075-1090
Author(s):  
Claude Daviau​ ◽  
Jacques Bertrand ◽  
Raymond Albert Ng
Keyword(s):  
Hydrogen Atom ◽  
Dirac Equation
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