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Relativistic Corrections to the Energy of the Electron in a Hydrogenlike Atom

В. В. Скобелев

Russian Physics JournalNov 1, 20172 citations

On the momentum representation of hydrogenic wave functions: Some properties and an application

J D Hey

The wave functions in momentum space for discrete states of hydrogenlike atoms are discussed in terms of both the early contributions to the subject and their present usefulness in atomic physics. The derivation of some of their important properties is outlined, in particular the expectation values of various powers of momentum and kinetic energy, and the kinetic energy distribution. As an application, the cross section for ionization of hydrogen in the metastable 2S state by electron impact is calculated with the aid of the binary-encounter approximation, which requires the use of momentum-space wave functions.The wave functions in momentum space for discrete states of hydrogenlike atoms are discussed in terms of both the early contributions to the subject and their present usefulness in atomic physics. The derivation of some of their important properties is outlined, in particular the expectation values of various powers of momentum and kinetic energy, and the kinetic energy distribution. As an application, the cross section for ionization of hydrogen in the metastable 2S state by electron impact is calculated with the aid of the binary-encounter approximation, which requires the use of momentum-space wave functions.

American Journal of PhysicsJan 1, 199339 citations

An alternative approach to calculating the mean values for relativistic hydrogen-like atoms

Wen-Chao Qiang, Yang Gao, Run‐Suo Zhou

Physics Letters ADec 9, 20047 citations

Expectation values and Fisher information theoretic measures of heavy flavoured mesons

E. Omugbe, Etido Patrick Inyang, Arezu Jahanshir +6 more

The expectation values play important role in atomic physics and quantum mechanics. They are vital to obtaining the quantum information theoretic measures, Compton profile, electronic kinetic energy, Langevin-Pauli diamagnetic susceptibility, Dirac exchange energy and so on. In this work, however, we utilized the bound state solutions of the non-relativistic Schrödinger equation under the Cornell potential to obtain the expectation values using two analytical methods such as the integral approach and the Hellmann-Feynman theorem method. We applied the mean values to obtain the Fisher information theoretic measures for the Charmonium and Bottomonium mesons. We found that the mean values and probability densities are sensitive to the meson masses and the principal quantum number for fixed orbital quantum states. The Dirac exchange and the kinetic energies obey the lowest bound inequalities for 3D atomic systems. Also, the results obey the Fisher uncertainty product, Cramer-Rao and the Heisenberg uncertainty inequalities for 3D quantum systems.The expectation values play important role in atomic physics and quantum mechanics. They are vital to obtaining the quantum information theoretic measures, Compton profile, electronic kinetic energy, Langevin-Pauli diamagnetic susceptibility, Dirac exchange energy and so on. In this work, however, we utilized the bound state solutions of the non-relativistic Schrödinger equation under the Cornell potential to obtain the expectation values using two analytical methods such as the integral approach and the Hellmann-Feynman theorem method. We applied the mean values to obtain the Fisher information theoretic measures for the Charmonium and Bottomonium mesons. We found that the mean values and probability densities are sensitive to the meson masses and the principal quantum number for fixed orbital quantum states. The Dirac exchange and the kinetic energies obey the lowest bound inequalities for 3D atomic systems. Also, the results obey the Fisher uncertainty product, Cramer-Rao and the Heisenberg uncertainty inequalities for 3D quantum systems.

Journal of the Nigerian Society of Physical SciencesDec 24, 20247 citations

Wave Functions for the Hydrogen-like Atom

WORLD SCIENTIFIC eBooksJan 1, 20260 citations

Classical physics derivation of quantization of electron elliptical orbit in hydrogenlike atom

Jiqing Zeng

On the basis of revising the quantum concept and reinterpreting Bohr's hydrogen atom structure model in classical physics, this paper deduces the elliptical orbital energy level formula of electrons in hydrogenlike atoms in detail. When the electron transition time is taken as unit time (1 s), the energy level formula is completely consistent with Bohr Sommerfeld's atomic structure theory.

Physics EssaysJun 10, 20221 citation

On the Mean Value of the Potential and Kinetic Energy of an Electron in a Hydrogenlike Atom

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