A preliminary experiment of determining the geopotential difference using two hydrogen atomic clocks and TWSTFT technique

General relativity theory(GRT)concludes that a precise clock ticks at different running rates if it is under the influence of different geopotentials.Therefore,by comparing the running rates of clocks at arbitrary two stations,the geopotential difference between them can be determined.In this study,with the help of two hydrogen atomic clocks(noted as H-masers),using the two-way satellite time and frequency transfer(TWSTFT)technique,we carried out experiments of the geopotential difference determination at the China Aerospace Science&Industry Corporation(CASIC),Beijing.Here the ensemble empirical mode decomposition(EEMD)method is adopted to remove periodic signals included in the original observations.Finally,the clock-comparison-determined geopotential difference in the experiments is determined.Results show that the difference between the geopotential difference determined by GRT and that determined by measuring tape is about 1316.1±931.0 m2s-2,which is equivalent to 134.3±95.0 m in height,and in consistence with the stability of the H-masers applied in the experiments(at the level of10-15/day).With the rapid improvement of atomic clocks’accuracy,the geopotential determination by accurate clocks is prospective,and it is promising to realize the unification of the world vertical height system(WVHS).

Emission Intensity in the Hydrogen Atom Calculated from a Non-Probabilistic Approach to the Electron Transitions

Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The calculation has been extended to all transitions between p and s states having main quantum numbers not exceeding 6. An evident similarity between the intensity pattern obtained from the Joule-Lenz law and the corresponding quantum-mechanical transition pro-babilities has been shown.

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters Er and Г/2 of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of 10^-9 - 10^-12 for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.

Interaction of intense laser pulses with hydrogen atomic clusters

The interaction between intense femtosecond laser pulses and hydrogen atomic clusters is studied by a simplified Coulomb explosion model. The dependences of average proton kinetic energy on cluster size, pulse duration, laser intensity and wavelength are studied respectively. The calculated results indicate that the irradiation of a femtosecond laser of longer wavelength on hydrogen atomic clusters may be a simple, economical way to produce highly kinetic hydrogen ions. The phenomenon suggests that the irradiation of femtosecond laser of longer wavelength on deuterium atomic clusters may be easier than that of shorter wavelength to drive nuclear fusion reactions. The product of the laser intensity and the squared laser wavelength needed to make proton energy saturated as a function of the squared cluster radius is also investigated. The proton energy distribution calculated is also shown and compared with the experimental data. Our results are in agreement with the experimental results fairly well.

Magic Wavelengths for the 1S-2S and 1S-3S Transitions in Hydrogen Atoms

The dynamic dipole polarizabilities for 1S, 2S and 3S states of the hydrogen atom are calculated using the finite B-spline basis set method, and the magic wavelengths for 1S-2S and 1S-3S transitions are identified. In comparison of the solutions from the Schr6dinger and Dirac equations, the relativistic corrections on the magic wavelengths are of the order of 10-2 nm. The laser intensities for a 300-Er-deep optical trap and the heating rates at 514 and 1371 nm are estimated. The reliable prediction of the magic wavelengths would be helpful for the experimental design on the optical trapping of the hydrogen atoms, and in turn, it would be helpful to improve the accuracy of the measurements of the hydrogen 1S-2S and 1S-3S transitions.

Time Intervals of the Electron Transitions between the Energy States in the Hydrogen Atom Calculated in a Non-Probabilistic Way

Definitions of the mechanical parameters entering the Bohr model of the hydrogen atom allowed us to calculate the time intervals connected with the electron transitions between the nearest-neighbouring energy levels in the atom. This is done in a strictly non-probabilistic way. The time results are compared with those derived earlier on the basis of the classical Joule-Lenz law for the energy emission adapted to the case of the electron transfer in the quantum systems. A similar formalism has been next applied to the harmonic oscillator and a particle moving in the one-dimensional potential box.

The Quantum Condition That Should Have Been Assumed by Bohr When Deriving the Energy Levels of a Hydrogen Atom

Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous quantum condition was not derived logically, but it beautifully explained the energy levels of the hydrogen atom. Therefore, Bohr’s quantum condition was accepted by physicists. However, the energy levels predicted by the eventually completed quantum mechanics do not match perfectly with the predictions of Bohr. For this reason, it cannot be said that Bohr’s quantum condition is a perfectly correct assumption. Since the mass of an electron which moves inside a hydrogen atom varies, Bohr’s quantum condition must be revised. However, the newly derived relativistic quantum condition is too complex to be assumed at the beginning. The velocity of an electron in a hydrogen atom is known as the Bohr velocity. This velocity can be derived from the formula for energy levels derived by Bohr. The velocity v of an electron including the principal quantum number n is given by αc/n. This paper elucidates the fact that this formula is built into Bohr’s quantum condition. It is also concluded in this paper that it is precisely this velocity formula that is the quantum condition that should have been assumed in the first place by Bohr. From Bohr’s quantum condition, it is impossible to derive the relativistic energy levels of a hydrogen atom, but they can be derived from the new quantum condition. This paper proposes raising the status of the previously-known Bohr velocity formula.

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

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.

Hydrogen Atom and Equivalent Form of the Lévy-Leblond Equation

We discuss the equivalent form of the Ldvy-Leblond equation such that the nilpotent matrices are two-dimensional. We show that this equation can be obtained in the non-relativistic limit of the （2＋1）-dimensional Dirac equation. Phrthermore, we analyze the case with four-dimensional matrices, propose a Hamiltonian for the equation in （3＋1） dimensions, and solve it for a Coulomb potential The quantized energy levels for the hydrogen atom are obtained, and the result is consistent with the non-relativistic quantum mechanics.

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

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.

Time of the Energy Emission in the Hydrogen Atom and Its Electrodynamical Background

The time of the energy emission between two neighbouring electron levels in the hydrogen atom has been calculated first on the basis of the quantum aspects of the Joule-Lenz law, next this time is approached with the aid of the electrodynamical parameters characteristic for the electron motion in the atom. Both methods indicate a similar result, namely that the time of emission is close to the time period of the electromagnetic wave produced in course of the emission. As a by-product of calculations, the formula representing the radius of the electron microparticle is obtained from a simple combination of the expressions for the Bohr magnetic moment and a quantum of the magnetic flux.

General calculation formulas and recurrence relations of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0

In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.

Adsorption of hydrogen atoms on Pd (211), (311) and (511) stepped defective surfaces

Using embedded-atom-method potential for Pd and MORSE potential for the interaction between H and Pd atoms, the adsorption properties of H atoms on Pd (211), (311) and (511) stepped defective surfaces were calculated systematically. For Pd (311) surface, it is found that the four-fold hollow sites H4 are the preferable sites for H atoms being adsorbed on these Pd defective surfaces. The sites H4 are the most stable adsorbed sites and the three-fold hollow sites Hf and Hh are metastable ones. The calculated results are in reasonable agreement with the HREELS experiment results. For the (211) and (511) stepped defective surfaces of Pd, our calculation shows that the most stable adsorption sites are H5 and H2 respectively, both of them are four fold hollow sites.

On Solvable Potentials, Supersymmetry, and the One-Dimensional Hydrogen Atom

The ways for improving on techniques for finding new solvable potentials based on supersymmetry and shape invariance has been discussed by Morales et al. [1] In doing so they address the peculiar system known as the one-dimensional hydrogen atom. In this paper we show that their remarks on such problem are mistaken. We do this by explicitly constructing both the one-dimensional Coulomb potential and the superpotential associated with the problem, objects whose existence are denied in the mentioned paper.

Gravitational Corrections to Energy-Levels of a Hydrogen Atom

氢原子 incentra 的精力层次的一阶的不安] 内部重力的地被调查。内部重力呸标志被原子核的团生产。精力移动与 Schwarzschild 度量标准为相对论的 1S， 2S， 2P,35， 3P， 3D， 4S，和 4P 层次被计算。计算结果证明重力的修正对全部的角动量量数字敏感。

Propterties of Coherent State for Hydrogen Atom

We construct the coherent state for the two-dimensional hydrogen atom,for which the averaged motion of position describes a Kepler ellipse.The coherent state can be expanded with respect to the eigenstates of 2D hydrogen atom,from which we evaluate the binding energy of the wave packet for this state.

Statistics and Correlation Properties of Diamagnetic High Rydberg Hydrogen Atom

在磁场的 Rydherg 氢原子的系列与 B 花键基础功能用线性变化方法被计算了[Acta Phys。罪恶。55 (2006 ) 3380 ] 。把我们关于高 Rydberg 精力层次做了一些统计分析的计算基于这些。近邻居的精力间距分发和 3 统计与是的磁场关于抗磁的 Rydberg 氢原子被显示出 0.6 T 和 6 T。多样地交叉的现象，多样地反生气，并且交叉混合了并且精力层次反生气出现在这份报纸。为两个盒子，在更低的精力的范围，精力水平统计性质关门到泊松分发。与增加精力，精力水平统计性质离开到泊松分发并且一步一步地趋于到 Wigner 分发。

Explicit expressions and recurrence formulas of radial average value for N-dimensional hydrogen atom

In this paper, two recurrence formulas for radial average values of N-dimensional hydrogen atom are derived. Explicit expressions for <n rJ N-2 |r s|n rJ N-2 > are given for 3≥s≥-6. These results can be applied to discuss average value of centrifugal potential energy and other physical quantities. The relevant results of the usual hydrogen atom are contained in more general conclusion of this paper as special cases.

Spectral Analysis for Fractional Hydrogen Atom Equation

In this paper, spectral analysis of fractional Sturm Liouville problem defined on (0, 1], having the singularity of type ?at zero and researched the fundamental properties of the eigenfunctions and eigenvalues for the operator. We show that the eigenvalues and eigenfunctions of the problem are real and orthogonal, respectively.

Spectra of Hydrogen Atom with GUP and Extra Dimensions

We argue that the Generalized Uncertainty Ptinciple (GUP) and the compact Extra dimensions will lead the hydrogen atom has the non bounded state spectra which equal the free particle in extra dimensions. We use Generalized Uncertainty Principle (GUP) to calculate the new energy spectra of hydrogen atom, and which lives in three dimensional Euclidean spaces with one extra dimension. The result is not familiar with our known before that En =0 when n is large enough. In our modified new spectra, we obtain that En,ι,0 = (1+2βι2/ρ2) ι2/2mρ2, which is lager than zero. These new spectra give us new method to obtain the existence of extra dimensions. Finally, we find that the spectra are same as part of extra dimensions in planck scale.