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

@article{Alavi2017DiracEH, title={Dirac equation, hydrogen atom spectrum and the Lamb shift in dynamical non-commutative spaces}, author={S. A. Alavi and Neda Rezaei}, journal={Pramana}, year={2017}, volume={88}, pages={1-5} }

We derive the relativistic Hamiltonian of hydrogen atom in dynamical non-commutative spaces (DNCS or Ο-space). Using this Hamiltonian we calculate the energy shift of the ground state as well the 2P1/2, 2S1/2 levels. In all the cases, the energy shift depends on the dynamical non-commutative parameter Ο. Using the accuracy of the energy measurement, we obtain an upper bound for Ο. We also study the Lamb shift in DNCS. Both 2P1/2 and 2S1/2 levels receive corrections due to dynamical nonβ¦Β

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## References

SHOWING 1-10 OF 41 REFERENCES

### Hydrogen atom spectrum and the lamb shift in noncommutative QED.

- PhysicsPhysical review letters
- 2001

The results show deviations from the usual QED both on the classical and the quantum levels, and on both levels, the deviations depend on the parameter of space/space noncommutativity.

### Dynamical noncommutative quantum mechanics

- Physics, Mathematics
- 2014

We study some basic and interesting quantum mechanical systems in dynamical noncommutative spaces in which the spaceβspace commutation relations are position dependent. It is observed that theβ¦

### Strings from position-dependent noncommutativity

- Mathematics
- 2010

We introduce a new set of noncommutative spacetime commutation relations in two space dimensions. The spaceβspace commutation relations are deformations of the standard flat noncommutative spacetimeβ¦

### Hyperfine splitting in noncommutative spaces

- Physics, Mathematics
- 2008

We study the hyperfine splitting in the framework of the noncommutative quantum mechanics (NCQM) developed in the literature. The results show deviations from the usual quantum mechanics. We showβ¦

### Relativistic Quantum Mechanics. Wave Equations

- Physics
- 1997

1. Relativistic Wave Equation for Spin-0 Particles: The Klein-Gordon Equation and Its Applications.- 2. A Wave Equation for Spin-1/2 Particles: The Dirac Equation.- 3. Lorentz Covariance of the Diracβ¦

### Quantum Mechanics in Noncommutative space

- Physics
- 2015

This paper provides an examination of how are prediction of standard quantum mechanic (QM) affected by introducing a noncommutative (NC) structure into the configuration space of the consideredβ¦

### Neutrino spin oscillations in gravitational fields in noncommutative spaces

- Physics
- 2015

We study neutrino spin oscillations in gravitational fields in noncommutative spaces. For the Schwarzschild metric the maximum frequency decreases as the noncommutativity parameter increases. In theβ¦

### Gravitational radiation in dynamical noncommutative spaces

- Physics, Mathematics
- 2015

We investigate gravitational radiation in dynamical noncommutative spaces. By including corrections to the gravitational potential due to dynamical noncommutativity, we calculate the power inβ¦

### Position-dependent noncommutativity in quantum mechanics

- Mathematics
- 2009

The model of the position-dependent noncommutativity in quantum mechanics is proposed. We start with given commutation relations between the operators of coordinatesβ¦