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Wave mechanics in quantum phase space: hydrogen atom

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Progress in Natural Science:Materials International 2007年第2期17卷 144-149页

作者： LU Jun ( Department of Foundational Science, Beijing Union University, Beijing 100101, China Department of Computational Science, National University of Singapore, Singapore 117543, Singapore) Department of Foundational Science Beijing Union University Beijing 100101 China Department of Computational Science National University of Singapore Singapore 117543 Singapore

The rigorous solutions of the stationary Schrodinger equation for hydrogen atom are solved with the wave-mechanics method within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The "Fourier-like" projection transformations of wave function from the phase space to position and momentum spaces are extended to three-dimensional systems. The eigenfunctions in general position and momentum spaces could be obtained through the transformations from eigenfunction in the phase space.

关键词： quantum phase space hydrogen atom projection transformation.

Deformed dispersion relation constraint with hydrogen atom 1S-2S transition

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Chinese Physics C 2020年第1期44卷 47-52页

作者： Jin Pu Guo-Ping Li Qing-Quan Jiang Xiao-Tao Zu School of Physics University of Electronic Science and Technology of ChinaChengdu 610054China College of Physics and Space Science China West Normal UniversityNanchong 637002China

We use the latest results of the ultra-high accuracy 1S-2S transition experiments in the hydrogen atom to constrain the forms of the deformed dispersion relation in the non-relativistic *** the leading correction of the non-relativistic limit,the experiment sets a limit at an order of magnitude for the desired Planck-scale level,thereby providing another example of the Planck-scale sensitivity in the study of the dispersion relation in controlled laboratory *** the next-to-leading term,the bound is two orders of magnitude away from the Planck scale,however it still amounts to the best limit,in contrast to the previously obtained bound in the non-relativistic limit from the cold-atom-recoil experiments.

关键词： deformed dispersion relation hydrogen atom transition experiment Planck-scale sensitivity

Properties of Coherent State for hydrogen atom

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Communications in Theoretical Physics 2003年第2期39卷 151-154页

作者： XuBO－Wei YEFei 等 DepartmentofPhysics ShanghaiJiaoTongUniversityShanghai200030China

We construct the coherent state for the two-dimensional hydrogen atom,for which the averaged motion of position describes a Kepler *** coherent state can be expanded with respect to the eigenstates of 2D hydrogen atom... 详细信息

关键词： coherent state hydrogen atom

Gravitational Corrections to Energy-Levels of a hydrogen atom

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Communications in Theoretical Physics 2007年第4期47卷 658-662页

作者： ZHAO Zhen-Hua LIU Yu-Xiao LI Xi-Guo Institute of Modern Physics the Chinese Academy of Sciences Lanzhou 730000 China Institute of Theoretical Physics Lanzhou University Lanzhou 730000 China

The first-order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number.

关键词： hydrogen atom gravitational perturbation generally covariant Dirac equation

Resolution in the Case of the hydrogen atom of an Improved Dirac Equation

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Journal of Modern Physics 2020年第7期11卷 1075-1090页

作者： Claude Daviau Jacques Bertrand Raymond Albert Ng Le Moulin de la Lande Pouillé-les-C&ocirc teaux France 15 Avenue Danielle Casanova Saint-Gratien France De La Salle University (DLSU) Manila Philippines

The improved Dirac equation is completely solved in the case of the hydrogen atom. A method of separation of variables in spherical coordinates is used. The angular functions are the same as with the linear Dirac equation: they account for the spin 1/2 of the electron. The existence of a probability density governs the radial equations. This gives all the quantum numbers required by spectroscopy, the true number of energy levels and the true levels obtained by Sommerfeld’s formula.

关键词： Electromagnetism Clifford Algebra Dirac Equation Lagrangian Formalism hydrogen atom

Relativistic Reduction of the Electron-Nucleus Force in Bohr’s hydrogen atom and the Time of Electron Transition between the Neighbouring Quantum Energy Levels

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Journal of Modern Physics 2020年第6期11卷 944-951页

作者： Stanisław Olszewski Institute of Physical Chemistry Polish Academy of Sciences Warsaw Poland

The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.

关键词： hydrogen atom The Bohr Model Lorentz Transformation Done with the Aid of the Electron Orbital Speed Maxwell Equation Applied to Calculate the Time Interval of Electron Transitions between Two Quantum Energy Levels Comparison with the Joule-Lenz Law for Energy Emission

Molecular Dynamics Simulation of Bombardment of hydrogen atoms on Graphite Surface

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Communications in Computational Physics 2008年第8期4卷 592-610页

作者： A.Ito H.Nakamura Department of Physics Graduate School of ScienceNagoya UniversityFuro-choChikusa-kuNagoya 464-8602Japan Department of Simulation Science National Institute for Fusion Science322-6 Oroshi-choToki 509-5292Japan

The new potential model of interlayer intermolecular interaction was proposed to represent“ABAB”stacking of *** bombardment of hydrogen atoms on the graphite surface was investigated using molecular dynamics *** the first graphene fromthe surface side was broken,the hydrogen atoms caused the following *** the case of the incident energy of 5 eV,many hydrogen atoms were adsorbed on the front of the first *** the case of the incident energy of 15 eV,almost all hydrogen atoms were reflected by the first *** the case of the incident energy of 30 eV,the hydrogen atoms were adsorbed between the first and second *** radial distribution function and the animation of the MD simulation demonstrated that the graphenes were peeled off one by one,which is called graphite *** C2H2 was generated in such chemical *** the other yieldedmolecules often had chain structures terminated by the hydrogen *** erosion yield increased linearly with time.

关键词： Plasma surface interaction chemical sputtering graphite graphene hydrogen atom

One Electron atom in Special Relativity with de Sitter Space-Time Symmetry

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Communications in Theoretical Physics 2012年第6期57卷 930-952页

作者：闫沐霖 Interdisciplinary Center for Theoretical Study Department of Modern PhysicsUniversity of Science and Technology of China

The de Sitter invariant Special Relativity （dS-SR） is SR with constant curvature, and a natural extension of usual Einstein SR （E-SR）. In this paper, we solve the dS-SR Dirac equation of hydrogen by means of the adiabatic approach and the quasi-stationary perturbation calculations of QM. hydrogen atom is located in the light cone of the Universe. FRW metric and ACDM cosmological model are used to discuss this issue. To the atom, effects of de Sitter space-time geometry described by Beltrami metric are taken into account. The dS-SR Dirac equation turns out to be a time dependent quantum Hamiltonian system. We reveal that：（i） The fundamental physics constants me, h, e variate adiabatically along with cosmologic time in dS-SR QM framework. But the fine-structure constant α≡ - e^2/（hc） keeps to be invariant; （ii）（2s^1/2 - 2p^1/2）-splitting due to dS-SR QM effects： By means of perturbation theory, that splitting △E（z） are calculated analytically, which belongs to O（1/R^2）-physics of dS-SR QM. Numerically, we find that when ｜R｜ = {103 Gly, 104 Gly, 105 Gly}, and z = {1, or 2}, the AE（z）〉〉 1 （Lamb shift）. This indicates that for these cases the hyperfine structure effects due to QED could be ignored, and the dS-SR fine structure effects are dominant. This effect could be used to determine the universal constant R in dS-SR, and be thought as a new physics beyond E-SR.

关键词： hydrogen atom special relativity with de sitter space-time symmetry time variation of physical constants Lamb shift time dependent Hamiltonian in quantum mechanics Friedmann-Robertson-Walker (FRW) universe

Circular Rydberg States of atomic hydrogen in an Arbitrary Magnetic Field

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Communications in Theoretical Physics 2011年第9期56卷 481-486页

作者：赵力波 B.C.Saha 杜孟利 Department of Physics Florida A & M UniversityTallahasseeFlorida 32307USA Institute of Theoretical Physics Chinese Academy of SciencesP.O.Box 2735Beijing 100190China

We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy of circular Rydberg states of hydrogen atoms in the intermediate magnetic field. This scheme can produce high accuracy energy levels and valid for an arbitrary magnetic field. Energy levels of hydrogen are presented for circular Rydberg states with azimuthal quantum numbers ｜m｜ =10-70 as a function of magnetic field strengths ranging from zero to 2.35 × 10^9 T. The variation of spatial distributions of electron probability densities with magnetic field strengths is discussed and competition between Coulomb and magnetic interactions is illustrated.

关键词： hydrogen atom circular Rydberg state magnetic field B-spline basis