The relativistic energy spectrum of hydrogen

Marsch, E.

doi:10.1002/andp.200410137

Cited by 9 publications

(61 citation statements)

References 13 publications

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“…Recently, by using Dirac's method, Marsch rigorously solved the hydrogen atom as a two-Dirac particle system bound by Coulomb force [34]. His solutions are composed of positive and negative pairs, corresponding respectively to hydrogen and anti-hydrogen as expected.…”

Section: Summary and Discussionmentioning

confidence: 99%

Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics

Ni¹,

Xu²,

Sen-Yue³

2011

Chinese Phys. B

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Based on the precision experimental data of energy-level differences in hydrogenlike atoms, especially the 1S-2S transition of hydrogen and deuterium, the necessity of establishing a reduced Dirac equation (RDE)with reduced mass as the substitution of original electron mass is stressed.The theoretical basis of RDE lies on two symmetries, the invariance under the space-time inversion and that under the pure space inversion. Based on RDE and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level )as the radiative correction on a bound electron staying in an off-mass-shell state-a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity. I. INTRODUCTION.As is well known, the Dirac equation for electron in a hydrogenlike atom is usually treated as a one-body equation with the nucleus being an inert core having infinite mass and exerting a potential V (r) = − (2)

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Section: Summary and Discussionmentioning

confidence: 99%

Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics

Ni¹,

Xu²,

Sen-Yue³

2011

Chinese Phys. B

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“…In a previous publication [1] the energy levels of a relativistic two-particle Hamiltonian for a binary (hydrogen-like) atom bound by the static Coulomb force were calculated exactly. Some derivations in this paper were not presented in sufficient detail.…”

Section: Eigenfunctions Of the Spin-orbit-coupling Operatorsmentioning

confidence: 99%

“…(48) of [1], where we also defined the two spin helicity operators: S r =Ŝ·r and I r =Î·r. They anticommute with their corresponding K-operators.…”

Section: Eigenfunctions Of the Spin-orbit-coupling Operatorsmentioning

confidence: 99%

“…At this point it is appropriate to continue with the operators being explicitly written in 4 × 4 matrix form, based on product states of the spin eigenfunctions [1]. The hermitian helicity operators can, according to their definitions, be written as:…”

Section: Eigenfunctions Of the Spin-orbit-coupling Operatorsmentioning

confidence: 99%

“…The operatorsK S andK I were similarly defined in eqs. (49-50) of paper [1]. We obtain them from eq.…”

Section: Eigenfunctions Of the Spin-orbit-coupling Operatorsmentioning

confidence: 99%

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The relativistic energy spectrum of hydrogen

Marsch¹

2006

Ann. Phys.

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The exact eigenfunctions of the spin-orbit-coupling operators for a relativistic binary system are calculated. Concerning the eigenvalue problem and the radial part of the wavefunction of the bound state, we provide corrections for our previous calculations [1] that contained some sign errors. Eigenfunctions of the spin-orbit-coupling operatorsIn a previous publication [1] the energy levels of a relativistic two-particle Hamiltonian for a binary (hydrogen-like) atom bound by the static Coulomb force were calculated exactly. Some derivations in this paper were not presented in sufficient detail. Especially the eigenfunctions of the spin-orbit-coupling operators,K I = 1 +L ·Î andK S = 1 +L ·Ŝ, were not calculated explicity, a task that will be completed in this supplement. The spin in units of /2 is denoted asŜ for the electron andÎ for the proton, andL = L/ refers to the orbital angular momentum with respect to the relative position vector r.To calculate the eigenfunctions we use the natural basis constructed by tensor products of the spin eigenvectors in eq. (48) Operator algebra shows that the spin orbit-coupling operators and spin helicity operators mutually do not commute with each other:and therefore cannot have common eigenfunctions. However, as shown below, one can construct common eigenfunctions ofK S andK I . Their common eigenvalue is called k. *

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References

2014

Relativistic Quantum Chemistry

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The relativistic energy spectrum of hydrogen

Cited by 9 publications

References 13 publications

Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics

Reduced Dirac equation and Lamb shift as off-mass-shell effect in quantum electrodynamics

The relativistic energy spectrum of hydrogen

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