Spectrum Of Hydrogen Atom Research Articles

Gauge-invariant description of a Dirac electron moving in a noncommutative gauge-field background

Abstract We provide a gauge invariant description of the quantum dynamics of an electron in a constant noncommutative (NC) gauge field background using the Dirac equation in an NC plane. We show that the physical force imparted on the electron is the standard Lorentz force but with modified NC magnetic fields that pick up two different first order corrections in the relativistic and non-relativistic (NR) domains. Taking NR limit of our Dira equation we show that noncommutativity affects the cyclotron frequency but leaves the Hall conductivity and cyclotron motion trajectory unaffected to first order in the NC parameter. The hyperfine splitting of Hydrogen atom (H-atom) spectrum also shows a first order correction.

A Rydberg-Bohr-de Broglie Algebraic Model of Hydrogen Atoms

Bohr ignored the electromagnetic interaction of moving charges in atoms and only considered Coulomb forces, thus encountering half frequency difficulties. This article considers the Lorentz force to make the classical Bohr model consistent with modern quantum theory, uses de Broglie's standing wave principle instead of Bohr's quantization assumption, derives the energy level formula for hydrogen atoms, and explains the radiation mechanism of hydrogen atomic spectra. The hydrogen atom in a spectral tube emits a photon wave train during one free path, and the wavelength of the photon is the eigen wavelength of its wave train. The head wavelength of the wave train is four thirds of its eigen wavelength, and the tail wavelength of the wave train is two-thirds of its eigen wavelength.

To the Theory of the Lamb Shift in the Relativistic Hydrogen Atom

Radiative corrections which remove the accidental degeneracy in the spectrum of the relativistic hydrogen atom and lead to the modification of the Coulomb law, are calculated within the novel approach, based on the exact solution of the Dirac equation with the Coulomb potential. The energy spectrum of the hydrogen atom is obtained with account for these corrections, and the Lamb shift is calculated for the lowest energy states.

Continuum spectrum of atomic lithium in a magnetic field of white dwarfs

ABSTRACT This paper reports on computational results of continuum spectra of atomic lithium in white-dwarf-strength magnetic fields. The adiabatic-basis-expansion method with R-matrix propagation has been used to study photoionization of magnetized alkali metal atoms. The R-matrix propagation technique and the two-dimensional matching scheme were utilized to obtain wavefunctions of the continuum states. Cross-sections of photoionization are calculated for lithium atoms in magnetic fields. Continuum spectra for its various bound-free transitions in magnetic white dwarf stars are presented as a function of field strengths ranging from 11.75 to 117.50 MG. Comparison is made between continuum spectra of diamagnetic hydrogen and lithium atoms. The comparison shows good agreement or remarkable difference for final continuum states with different symmetries in the photoionization processes concerned. A detailed analysis has been performed to understand the obtained results. The good agreement displayed manifests the reliability of the extended adiabatic-basis-expansion method. This method is suited to produce a large number of photoionization cross-section data for alkali metal atoms in a strong magnetic field, and therefore can serve as a tool to simulate continuum spectra observed in the atmospheres of magnetic white dwarfs with alkali metal atoms.

Dynamically enhanced Autler–Townes splitting by orthogonal XUV fields

Abstract Based on numerical solutions of the time-dependent Schrödinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally polarized laser pulses with a relative time delay in a pump–probe configuration. The pump pulse resonantly excites electrons from the 1s and 2p levels, inducing Rabi oscillations. The resulting dynamically enhanced Autler–Townes (AT) splitting is observed in the photoelectron energy spectrum upon interaction with the second probe pulse. In contrast to the previous parallel-polarization scheme, the proposed orthogonal-polarization configuration enables the resolution of dynamically enhanced AT splitting over a considerably wider range of probe photon energies.

Time-resolved subcycle and intercycle interference influenced momentum shift in nonadiabatic tunnelling ionization

Time-resolved subcycle and intercycle interference influenced momentum shift in nonadiabatic tunnelling ionization

Lyman- Spectra shapes in high redshift and low redshift galaxies

Lyman-alpha (Ly) photons were first predicted by Theodore Lyman in 1906 as part of his work on the hydrogen atom spectrum. The Ly transition occurs when an electron in a hydrogen atom falls from the second energy level to the ground state, releasing a photon with a wavelength of 121.6 nanometres. It was not until the 1960s that Ly photons were observed in astronomical sources, including galaxies and quasars. Since then, the Ly line has been recognized as a powerful probe of the intergalactic medium and the properties of galaxies, providing insights into the formation and evolution of structures in the universe. With the development of advanced telescopes and spectrographs, astronomers have been able to study Ly photons in greater detail and at higher redshifts. This has led to new discoveries and a deeper understanding of the universe, including the epoch of reionization and the formation of the first galaxies. Today, Ly studies continue to be an active area of research, with the potential to uncover even more insights into the nature and history of the cosmos. Ly spectral shapes are a crucial tool for unravelling the mysteries of the universe. These spectra provide valuable information about the distribution of gas and the physical properties of galaxies at different epochs. By analysing Ly spectra from galaxies with low and high redshifts, astronomers can gain insights into the formation and evolution of galaxies and the process of cosmic reionization.

Potential energy surfaces for electron dynamics from a model of localized Gaussian wave packets with valence-bond spin-coupling: High-harmonic generation spectra from H and He atoms

Potential energy surfaces for electron dynamics from a model of localized Gaussian wave packets with valence-bond spin-coupling: High-harmonic generation spectra from H and He atoms

A Single Photo for Calibration and Measurement: A Low-Cost Spectrometry Setup

In the last decades spectroscopy began to play an essential role in physics education research with the recognition that atomic spectra constitute a good occasion to study the concepts of quantum mechanics. Moreover, activities in which atomic spectra are studied in order to understand star structure and evolution have proved particularly engaging for students. In this sense, the hydrogen atom spectrum is especially important in astronomy. Other researchers showed how interdisciplinary experimental activities involving interferometry and applied optics offer a good occasion to teach fundamental concepts of radiation-matter interaction.

Investigation and diagnostics of plasma flows in a pulsed plasma accelerator for experimental modelling of processes in tokamaks

This paper presents the experimental results on electron, ion temperatures and densities in a pulsed plasma accelerator. The values of electron densities and temperatures were computed using the methods of relative intensities of Hα and Hβ lines, Hβ Stark broadening, and the technique is based on Faraday cup beam current measurements. In this work, a linear optical spectrometer S-100 was used to acquire the emission spectra of hydrogen and air plasmas. In this spectrum, there are some lines due to Fe, Cu, N2, O2, and H2. The series of visible lines in the hydrogen atom spectrum are named the Balmer series. The spectral emissions of iron and copper occur throughout the gas breakdown and ignition of an arc discharge, during the erosion and sputtering of materials. The vacuum chamber and coaxial electrodes were made. The electron temperatures and densities in a pulsed plasma accelerator, measured via relative intensities of spectral lines and Stark broadening, at a charging voltage of a capacitor bank of 3 kV and a working gas pressure in a vacuum chamber of 40 mTorr, were 2.6 eV and 1.66 · 1016 cm−3 for hydrogen plasma. These results were compared with the Faraday cup beam current measurements. However, no match was found. Considering and analyzing this distinction, we concluded that the spectral method of plasma diagnostics provides more accurate results than electrical measurement. The theory of probe measurements can give approximate results in a moving plasma.

A Review of the Bohr’s Model of Hydrogen Atom

In this paper, the classical Bohr’s model of the hydrogen atom has been revisited. Two values of fundamental physical properties of an electron in the hydrogen atom has been identified. These physical properties ( & ) are constant in nature. The aim for the review was to contribute to the solution of disagreement between the Bohr’s wavelength ( ) and the Balmer’s experimental observation ( ) for the emission spectrum of hydrogen atom. There are two other constants and that were identified in the Bohr’s equation of the hydrogen atom.
 The four fundamental physical constants are intrinsic properties of an electron and can be applied to multi-electron system. They can also be obtained from Schrodinger’s equation for hydrogen atom at steady state. These constants may be subjected to scrutiny for their determination for better understanding. Also, since Bohr’s model of hydrogen atom is based on classical mechanics, this paper has provided an alternate method of solving simple problems in atomic physics under Bohr’s model to aid good mental picture of hydrogen atom to scientists.

The unidentified infrared bands and the spectrum of atomic hydrogen

This letter compares the footprints on a spectral axis of the main unidentified infrared emission bands (UIBs) with the recombination lines of atomic hydrogen. The comparison shows striking correspondences, suggesting that atomic hydrogen may be involved in the production of UIBs.

Quantum impedance Lorentz oscillator and its 1- and 2-photon-absorption applications

In this paper, a classical Lorentz oscillator is quantized via Bohr–Sommerfeld quantum theory and 1- and 2-photon absorption (1PA and 2PA) selection rules of quantum mechanics. Based on the Bohr–Sommerfeld model of a hydrogen-like atom in the adiabatic approximation, the computational formulas of the linear and nonlinear parameters and the damping coefficient of the quantized oscillator are derived and further expressed in terms of microphysical quantities, such as electronic charge and mass, Bohr radius, and effective quantum number. In accordance with Boltzmann thermal equilibrium distribution, here, the atom number density in general electric susceptibility is changed to the energy level transition one from the initial to the final state at equilibrium between atomic emission and absorption under light field. A new relationship is proposed to determine the transition eigenfrequency according to the peak frequency and full width at half maximum of an absorption spectrum. Our theoretical simulations of the 1PA spectra of atomic hydrogen and lithium and 1PA and 2PA spectra of two kinds of organic molecules turn out to be in good agreement with the experimental ones. These results suggest that our advancement in the quantization of the Lorentz oscillator is likely successful to make it available for use in the quantitative description of atomic or molecular 1PA and 2PA processes. Generally, the improved Lorentz oscillator may also be more suitable for approximating both linear and nonlinear properties of many dielectric or optoelectronic materials due to its relative simplicity.

Computer algebra in physics: The hidden SO(4) symmetry of the hydrogen atom

Computer algebra in physics: The hidden SO(4) symmetry of the hydrogen atom

Probing anharmonic phonons by quantum correlators: A path integral approach.

We devise an efficient scheme to determine vibrational properties from Path Integral Molecular Dynamics (PIMD) simulations. The method is based on zero-time Kubo-transformed correlation functions and captures the anharmonicity of the potential due to both temperature and quantum effects. Using analytical derivations and numerical calculations on toy-model potentials, we show that two different estimators built upon PIMD correlation functions fully characterize the phonon spectra and the anharmonicity strength. The first estimator is associated with the force-force quantum correlators and, in the weak anharmonic regime, yields reliable zero-point motion frequencies and thermodynamic properties of the quantum system. The second one is instead connected to displacement-displacement correlators and accurately probes the lowest-energy phonon excitations, regardless of the anharmonicity strength of the system. We also prove that the use of generalized eigenvalue equations, in place of the standard normal mode equations, leads to a significant speed-up in the PIMD phonon calculations, both in terms of faster convergence rate and smaller time step bias. Within this framework, using ab initio PIMD simulations, we compute phonon dispersions of diamond and of the high-pressure I41/amd phase of atomic hydrogen. We find that in the latter case, the anharmonicity is stronger than previously estimated and yields a sizeable red-shift in the vibrational spectrum of atomic hydrogen.

Natural and magnetically induced entanglement of hyperfine-structure states in atomic hydrogen

The spectrum of atomic hydrogen has long been viewed as a Rosetta stone that bears the key to decode the writings of quantum mechanics in a vast variety of physical, chemical, and biological systems. Here, we show that, in addition to its role as a basic model of quantum mechanics, the hydrogen atom provides a fundamental building block of quantum information. Through its electron and nuclear spin degrees of freedom, the hydrogen atom is shown to lend a physically meaningful frame and a suitable Hilbert space for bipartite entanglement, whose two-qubit concurrence and quantum coherence can be expressed in terms of the fundamental physical constants -- the Planck and Boltzmann constants, electron and proton masses, the fine-structure constant, as well as the Bohr radius and the Bohr magneton. The intrinsic, natural entanglement that the hyperfine-structure (HFS) states of the H atom store at low temperatures rapidly decreases with a growth in temperature, vanishing above a $\tau_c$ $\approx$ 5.35 $\mu$eV threshold. An external magnetic field, however, can overcome this thermal loss of HFS entanglement. As one of the central findings of this work, we show that an external magnetic field can induce and sustain an HFS entanglement, against all the odds of thermal effects, at temperatures well above the $\tau_c$ threshold, thus enabling magnetic-field-assisted entanglement engineering in low-temperature gases and solids.

Effect of Variations in the Extended Hydrogen Corona of Mars on the Efficiency of Charge Exchange with Solar Wind Protons

This paper presents the results of calculating the efficiency of solar wind proton charge exchange as a function of variations in the column density of hydrogen atoms in the extended corona of Mars. The presence of regular density variations has been known for a long time and has been associated with the change of seasons on Mars. However, sporadic density variations in the upper Martian atmosphere were detected recently as well. They were caused by various processes in the underlying atmosphere, such as ejection of water vapor and ice particles at altitudes up to 100 km due to global dust storms, which was discovered in the Mars Express and MAVEN observations. Taking into account the variations in the column density with the observed amplitude up to one order of magnitude is absolutely necessary to correctly consider the interaction of solar wind protons with the Martian atmosphere. The calculations using the kinetic Monte Carlo model revealed that with a 2- and 5-fold increase in the column density of H atoms in the corona of Mars, the charge exchange efficiency also increases and reaches 6% and 8%, respectively, as compared to the base value of 4%. The energy spectrum of hydrogen atoms penetrating into the Martian atmosphere does not change and remains identical in structure to the spectrum of undisturbed solar wind protons. These estimates, combined with the previously developed kinetic model of the proton and hydrogen atom precipitation into the planetary atmosphere, make it possible to do the following: to trace all the stages of the penetration of the undisturbed solar wind protons into the dense layers of the atmosphere, as well as interpret the observed characteristics of proton auroras depending on the variations of atomic hydrogen content in the Martian corona.

Positive-energy spectra of atomic hydrogen in a magnetic field: A comparative study between different theoretical approaches

The problem of photoionization of atomic hydrogen in a white-dwarf-strength magnetic field is revisited to understand the existing discrepancies in the positive-energy spectra obtained by a variety of theoretical approaches reported in the literature. Oscillator strengths for photoionization are calculated with the adiabatic-basis-expansion method developed by Mota-Furtado and O'Mahony [Phys. Rev. A {\bf 76}, 053405 (2007)]. A comparative study is performed between the adiabatic-basis-expansion method and our previously developed coupled-channel theory [Phys. Rev. A {\bf 94}, 033422 (2016)]. A detailed analysis of the positive-energy spectra obtained here and those from other theoretical approaches shows that the adiabatic-basis-expansion method can produce more accurate positive-energy spectra than other reported approaches for low field strengths.

Energy level splitting of a 2D hydrogen atom with Rashba coupling in non-commutative space

We explore the non-commutative (NC) effects on the energy spectrum of a two-dimensional hydrogen atom. We consider a confined particle in a central potential and study the modified energy states of the hydrogen atom in both coordinates and momenta of non-commutativity spaces. By considering the Rashba interaction, we observe that the degeneracy of states can also be removed due to the spin of the particle in the presence of NC space. We obtain the upper bounds for both coordinates and momenta versions of NC parameters by the splitting of the energy levels in the hydrogen atom with Rashba coupling. Finally, we find a connection between the NC parameters and Lorentz violation parameters with the Rashba interaction.

Square Roots of Kepler Ellipses, Electrons and Rydberg Atoms in a Magnetic Field

Young Kepler’s daring ideas on the structure of the Solar system are applied to the analysis of planetary distances in the exoplanetary system HD 10180. Using Zhukovsky’s transformation, the essence of the spinor regularization of Kepler’s problem is explained as extracting the square root of an ellipse and using a Kepler eccentric anomaly instead of the usual time. The achievements of Kharkiv radio astronomers in the search for radio recombination lines of Rydberg carbon atoms at the UTR-2 radio telescope are considered. A generalized spinor regularization of the Kepler problem is used to analyze the energy spectra of Rydberg hydrogen atoms in a magnetic field.