Energy Levels Of Hydrogen Atom Research Articles

Dipole sum rules of a hydrogen atom in a Debye-Hückel plasma

In this work, we carry out a study of the dipole oscillator strength sum rule, Sk, and the logarithmic, Lk, version, for a hydrogen atom embedded in a Debye-Huckel plasma. We solve the time-independent Schrodinger equation by means of a finite-differences approach to obtain the discrete and continuum spectrum of the atom embedded in the plasma, as a function of the screening parameter, λD. We find excellent agreement for the Sk and Lk sum rules for λD → ∞, i.e., no plasma, in comparison with exact theoretical results. For plasma interaction, we obtain the conditions for the delocalization of the hydrogen atom energy levels finding its effects on the Sk sum rules. We find that for k ≤ 0, Sk increases as the screening constant decreases until λ ~ 0.84 a.u., where the 1s ground state becomes delocalized due to the plasma weakening. For the static dipole polarizability, S−2, we find excellent agreement of our results for the discrete and continuum spectrum to available data in the literature for selected values of screening parameters. In the logarithmic counterpart, Lk, the sum rules decrease for lower values of the screening length for k ≤ 0. We observe a decrease of the mean excitation energy, I0 = eL0/S0, as the screening length decreases finding a sudden change for λD ~ 2 a.u. Furthermore, we obtain closure relations for the Sk sum rule with k = −1, 1, 2, 3 as a function of the Debye-Huckel screening and find excellent agreement with the sum over excited states for k = −1, 0, 1, and 2 and find that S3 sum rule diverges for a hydrogen atom immersed in a Debye-Huckel plasma. We conclude that the fulfillment of the closure relations requires a good description of the excitation states.

Noncommutative phase space with rotational symmetry and hydrogen atom

We construct algebra with noncommutativity of coordinates and noncommutativity of momenta which is rotationally invariant and equivalent to noncommutative algebra of canonical type. Influence of noncommutativity on the energy levels of hydrogen atom is studied in rotationally invariant noncommutative phase space. We find corrections to the levels up to the second order in the parameters of noncommutativity and estimate the upper bounds of these parameters.

A quantum Monte Carlo study of confined quantum systems: application to harmonic oscillator and hydrogenic-like atoms

The correlation function quantum Monte Carlo (CFQMC) approach is employed to study the energy spectra of confined quantum systems. This method, applied originally to determine rovibrational eigenenergies of molecules, is utilized here to calculate the energy levels of hydrogen atom, helium cation, lithium dication and two confined harmonic oscillator (HO) models: the one-dimensional HO within a box of impenetrable walls and the three-dimensional one confined by an impenetrable spherical box. The dependence of the eigenenergies on functional form and the number of the basis functions are analyzed for various confinement parameters. The present results are compared with those previously published, and the efficiency of the CFQMC method to treat confined quantum systems is discussed.

Corrections to the energy levels of hydrogen atom in space with spin noncommutativity of coordinates

Corrections to the energy levels of hydrogen atom in space with spin noncommutativity of coordinates

On the Heisenberg and Schrödinger Pictures

A quantum theory for a one-electron system can be developed in either Heisenberg picture or Schrodinger picture. For a many-electron system, a theory must be developed in the Heisenberg picture, and the indistinguishability and Pauli’s exclusion principle must be incorporated. The hydrogen atom energy levels are obtained by solving the Schrodinger energy eigenvalue equation, which is the most significant result obtained in the Schrodinger picture. Both boson and fermion field equations are nonlinear in the presence of a pair interaction.

Aspects of electrodynamics modified by some dimension-five Lorentz-violating interactions

Assuming Lorentz symmetry is broken by some fixed vector background, we study the spinor electrodynamics modified by two dimension-five Lorentz-violating interactions between fermions and photons. The effective polarization and magnetization are identified from the modified Maxwell equations, and the theoretical consequences are investigated. We also compute the corrections to the relativistic energy levels of hydrogen atom induced by these Lorentz-violating operators in the absence and presence of uniform external fields in first-order perturbation theory. We find that the hydrogen spectrum is insensitive to the breakdown of Lorentz boost symmetry.

Vacuum polarization corrections in energy levels of hydrogen atom

A numerical calculation of the one photon vacuum polarization corrections in 1s, 2s, 2p, 3s, 3p and 3d energy levels of hydrogen atom is presented using Schrodinger solutions taking the Uehling potential as a correction. The relativistic effect on 1s, 2s, 2�� 1 2 and 2�� 3 2 levels are calculated by using Dirac wave functions in the presence of Coulomb potential. The contribution of this correction decreases with the increase in principle quantum number �� and orbital quantum number �� . Keywords: Vacuum polarization correction, hydrogen atom, Uehling potential

Modification of the coulomb law and energy levels of hydrogen atom in superstrong magnetic field

The screening of a Coulomb potential by superstrong magnetic field is studied. Its influence on the spectrum of a hydrogen atom is determined.

Quarkonium and hydrogen spectra with spin-dependent relativistic wave equation

A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to spin-orbit interaction and for the additional potential energy due to spin and spin-orbit coupling. Spin angular momentum operator is integrated into the equation of motion. This requires modification to classical Laplacian operator. Consequently the Dirac matrices and the k operator of Dirac's theory are dispensed with. The theory points out that the curvature of the orbit draws on certain amount of kinetic and potential energies affecting the momentum of electron and the spin-orbit interaction energy constitutes a part of this energy. The theory is developed for spin 1/2 bound state single electron in Coulomb potential and then further extended to quarkonium physics by introducing the linear confining potential. The unique feature of this quarkonium model is that the radial distance can be exactly determined and does not have a statistical interpretation. The established radial distance is then used to determine the wave function. The observed energy levels are used as the input parameters and the radial distance and the string tension are predicted. This ensures 100% conformance to all observed energy levels for the heavy quarkonium.

Energy Levels of "Hydrogen Atom" in Discrete Time Dynamics

We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are able to reconstruct potential which in discrete time formalism leads to energy levels of unperturbed hydrogen atom. We also consider linear energy levels of quantum harmonic oscillator and show how they are produced in the discrete time formalism. More generally, we show that in discrete time formalism finite motion in central potential leads to discrete energy spectrum, the property which is common for quantum mechanical theory. Thus deterministic (but discrete time!) dynamics is compatible with discrete energy levels.

Laser-spectroscopic methods for diagnostics of electric fields in plasma (review)

Methods for measuring electric fields in plasma based on laser spectroscopy and the Stark effect on Rydberg atomic levels and rotational levels of polar diatomic molecules are considered. These methods feature high sensitivity and allow measurements of both static and alternating electric fields in plasma with high temporal and spatial resolutions. It is shown that laser-spectroscopic techniques also allow measurements of relatively weak magnetic fields in plasmas of facilities with magnetic plasma confinement. Such measurements can be based on the use of Stark splitting of highly excited energy levels of hydrogen atoms in a Lorentzian electric field, while a decrease in the fluorescent-radiation intensity at the Balmer-α line can serve as a recorded signal.

Effective interactions and the hydrogen atom

The technique of effective interactions, which has become commonplace in contemporary particle/nuclear physics, is used to analyze the structure of hydrogen atom energy levels.

A New Pseudospectral Method for Calculations of Hydrogen Atom in Arbitrary External Fields

A new pseudospectral method was introduced to calculate wavefunctions and energy levels of hydrogen atom in arbitrary potential. Some results of hydrogen atom in uniform magnetic fields were presented, high accuracy of results was obtained with simple calculations, and our calculations show very fast convergence. It suggests a new method for calculations of hydrogen atom in external fields.

The Photoionization of Atomic Hydrogen in an Intense Circularly Polarized Laser Field**The project supported by National Natural Science Foundation of China under Grant No. 10075004

We calculate nonperturbatively the irfluence of a strong circularly polarized laser beam on the hydrogen atom energy levels by making use of the time-independent formalism proposed by one of us. The photoionization cross section of the hydrogen atom irradiated by this laser beam and the angular distribution of photoelectrons are also calculated. From the numerical results we clearly see the intensity dependence of the whole photoionization process,including the intensity dependence of the photoelectron energies.

AN ALTERATIVE METHOD OF ADIABATIC VARIATIONAL CALCULATION OF HYDROGEN ENERGY IN A STRONG MAGNETIC FIELD

In this article,by using the adiabatic approximation and variational principle and introducing an effective potential we have computed some energy levels of hydrogen atom in the presence of a strong magnetic field(1≤β≤2000) and compared our results with the like multi-configuration Hartree-Fock method.We found a basic function with better convergence than the Landau function.

Hydrogen metrology: up to what limit?

Improvements in the experimental measurement of energy levels of Hydrogen atom, obtained from the Laser Doppler-free techniques. Review of recent progresses in theoretical calculations, and comparisons.

Motion and ionization equilibrium of hydrogen atoms in a superstrong magnetic field.

We study the effects of finite proton mass on the energy levels of hydrogen atoms moving transverse to a superstrong magnetic field B with generalized pseudomomentum ${\mathit{K}}_{\mathrm{\ensuremath{\perp}}}$. Field strengths of order B\ensuremath{\sim}${10}^{12}$ G are typically found on the surfaces of neutron stars, but we also study the regime B\ensuremath{\gtrsim}${\mathit{B}}_{\mathit{crit}}$=4.23\ifmmode\times\else\texttimes\fi{}${10}^{13}$ G, where the Landau excitation energy of the proton is large. We adopt two different approaches to the two-body problem in strong magnetic fields and obtain an approximate but complete solution of the atomic energy as a function of B and ${\mathit{K}}_{\mathrm{\ensuremath{\perp}}}$. We show that, for B\ensuremath{\gg}${\mathit{B}}_{\mathit{crit}}$, there is an orthogonal set of bound states that do not have any Landau excitation contribution in their energies. The states with very large ${\mathit{K}}_{\mathrm{\ensuremath{\perp}}}$ have small binding energies and small transverse velocities, but are nevertheless distinct from the fully ionized states. The final results for the excitation energies are given in the form of analytical fitting formulas. The generalized Saha equation for the ionization-recombination equilibrium of hydrogen gas in the presence of a superstrong magnetic field is then derived. Although the maximum transverse velocity of a bound atom decreases as B increases, the statistical weight due to transverse motion is actually increased by the strong magnetic field. For the astrophysically interesting case of relatively low density and temperature, we obtain analytic approximations for the partition functions. The highly excited bound states have a smaller statistical weight than the fully ionized component.

From [formula omitted] algebra to κ-Lorentz quasigroup. A deformation of relativistic symmetry

We consider an algebraic ansatz for the class of nonlinear D=4 Poincaré algebras and show that it contains only the quantum κ- Poincar e ́ (real Hopf) algebras, obtained recently by the contraction of U q (O(3,2)). We derive the explicit formulae for the finite κ-Lorentz transformations generated by the realizations of the κ- Poincar e ́ algebra in D=4 momentum space. These finite κ-Lorentz transformations form a quasigroup, with generalized composition law of the boost parameters (rapidities). We consider further the (2 s+1)-component field realizations with arbitrary spin s and their finite κ-Lorentz transformations. For s= 1 2 we obtain the κ-covariant Dirac equation, derived from the finite κ-Lorentz boost formula. After the coupling of the κ-deformed Dirac equation to the electromagnetic potential we show that in the lowest order (linear) in el/ κ the κ-corrections to the hydrogen atom energy levels vanish but the value g=2 of the electron's magnetic moment is modified ( g=2→ g=2[1+( m el / κ)]. Finally the space-time description of κ-relativistic fields is briefly discussed.

Dirac equation and energy levels of hydrogenlike atoms in Robertson-Walker metric

The Dirac equation of the hydrogenlike atom in the Robertson-Walker metric is studied in this paper by means of tetrad formalism. The decoupled Dirac equation is derived and energy levels of hydrogen atoms taking into account the cosmological radius are obtained by using the perturbation expansion.

Zeeman effect in the hydrogen atom

The authors consider analytic expressions for the energy levels of hydrogen atoms in the presence of a magnetic field which incorporate the asymptotic behaviour, the large-order behaviour of the perturbation series and the first few coefficients of the series. The authors obtain the large-order behaviour from Bender-Wu theory by evaluating the decay probability using the one-dimensional WKB method.