Hydrogen atom in strong magnetic field revisited

Two-dimensional hydrogen-like atom in a weak magnetic field

We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schrödinger perturbation theory, using the Sturmian expansion of the generalized radial Coulomb Green function, we derive explicit analytical expressions for corrections to an arbitrary planar hydrogenic bound-state energy level, up to the fourth order in the strength of the perturbing magnetic field. In the case of the ground state, we correct an expression for the fourth-order correction to energy available in…

A simple model for a minimal environment: the two-atom Tavis-Cummings model revisited

Individual quantum systems may be interacting with surrounding environments having a small number of degrees of freedom. It is therefore relevant to understand the extent to which such small (but uncontrollable) environments could affect the quantum properties of the system of interest. Here we discuss a simple system-environment toy model, constituted by a two-level atom (atom 1) interacting with a single mode cavity field. The field is also assumed to be (weakly) coupled to an external noisy subsystem, the small environment, modeled as a second two-level atom (atom 2). We investigate the act…

Lorentz atom revisited by solving Abraham-Lorentz equation of motion

By solving the non-relativistic Abraham-Lorentz (AL) equation, I demonstrate that AL equation of motion is not suited for treating the Lorentz atom, because a steady-state solution does not exist. The AL equation serves as a tool, however, for deducing appropriate parameters $Ω,Γ$ to be used with the equation of forced oscillations in modelling the Lorentz atom. The electric polarizability, which many authors "derived" from AL equation in recent years, is found to violate Kramers-Kronig relations rendering obsolete the extracted photon-absorption rate, for example. Fortunately, errors turn out…

圆偏振激光存在下类氢原子的动态 Stark 位移

Dynamic Stark shift of Hydrogen-like atoms in the presence of circularly polarized laser light

本文结合经典绝热阻尼框架与二次量子化偶极相互作用的不含时微扰论，解析推导圆偏振激光下类氢体系的动态 AC Stark 位移，并证明两种方法在大光子数极限下给出相同公式。

Off-diagonal geometric phase of atom-electron coupling in hydrogen atom

In this paper, the off-diagonal geometric phase of thermal state in hydrogen atom under the effects of external magnetic field is considered. Increasing temperature tends to suppress the off-diagonal geometric phase, including 1-order and 2-order cases. On the other hand, the relationship between the geometric phase and external magnetic field is discussed.

Hydrogen atom in phase space: The Wigner representation

We have found an effective method of calculating the Wigner function, being a quantum analogue of joint probability distribution of position and momentum, for bound states of nonrelativistic hydrogen atom. The formal similarity between the eigenfunctions of nonrelativistic hydrogen atom in the momentum representation and Klein-Gordon propagators has allowed the calculation of the Wigner function for an arbitrary bound state of the hydrogen atom. These Wigner functions for some low lying states are depicted and discussed.

Perturbation hydrogen-atom spectrum in deformed space with minimal length

We study energy spectrum for hydrogen atom with deformed Heisenberg algebra leading to minimal length. We develop correct perturbation theory free of divergences. It gives a possibility to calculate analytically in the 3D case the corrections to $s$-levels of hydrogen atom caused by the minimal length. Comparing our result with experimental data from precision hydrogen spectroscopy an upper bound for the minimal length is obtained.

Dispersion of Klauder's temporally stable coherent states for the hydrogen atom

We study the dispersion of the "temporally stable" coherent states for the hydrogen atom introduced by Klauder. These are states which under temporal evolution by the hydrogen atom Hamiltonian retain their coherence properties. We show that in the hydrogen atom such wave packets do not move quasi-classically; i.e., they do not follow with no or little dispersion the Keplerian orbits of the classical electron. The poor quantum-classical correspondence does not improve in the semiclassical limit.

Hydrogen atom in phase space. The Kirkwood-Rihaczek representation

We present a phase-space representation of the hydrogen atom using the Kirkwood-Rikaczek distribution function. This distribution allows us to obtain analytical results, which is quite unique because an exact analytical form of the Wigner functions corresponding to the atom states is not known. We show how the Kirkwood-Rihaczek distribution reflects properties of the hydrogen atom wave functions in position and momentum representations.

On the q-analogue of the hydrogen atom

The discrete spectrum of a q-analogue of the hydrogen atom is obtained from a deformation of the Pauli equations. As an alternative, the spectrum is derived from a deformation of the four-dimensional oscillator arising in the application of the Kustaanheimo-Stiefel transformation to the hydrogen atom. A model of the 2s-2p Dirac shift is proposed in the context of q-deformations.

Coherent States for the Hydrogen Atom

The long-standing problem of finding coherent states for the (bound state portion of the) hydrogen atom is positively resolved. The states in question: (i) are normalized and are parameterized continuously, (ii) admit a resolution of unity with a positive measure, and (iii) enjoy the property that the temporal evolution of any coherent state by the hydrogen atom Hamiltonian remains a coherent state for all time.

再探 Duan-Kimble 腔–原子量子存储器加载方案

The Duan-Kimble cavity-atom quantum memory loading scheme revisited

本文纠正 Duan-Kimble 方案中单光子反射率函数的误用，并提出将光子与腔调谐至原子共振中点的 push-pull 构型，以更高保真度和预示概率改进量子存储器加载。

含自旋的氢原子中的$SO(4)$对称性

$SO(4)$ Symmetry in Hydrogen Atom with Spin

本研究将量子Runge-Lenz矢量推广为自旋依赖形式，基于$SO(4)$对称性推导含自旋氢原子的新哈密顿量并确定其能谱，拓展了氢原子研究基础，可为相关复杂模型提供参考。

Geometrical phase of thermal state in hydrogen atom

In this paper, the geometric phase of thermal state in hydrogen atom under the effects of external magnetic field is considered. Especially the effects of the temperature upon the geometric phase is discussed. Also we discuss the time evolution of entanglement of the system. They show some similar behaviors.

Exact Solution of the Klein-Gordon Equation for the Hydrogen Atom Including Electron Spin

The term describing the coupling between total angular momentum and energy-momentum in the hydrogen atom is isolated from the radial Dirac equation and used to replace the corresponding orbital angular momentum coupling term in the radial K-G equation. The resulting spin-corrected K-G equation is a second order differential equation that contains no matrices. It is solved here to generate the same energy eigenvalues for the hydrogen atom as the Dirac equation.

Hénon-Heiles Interaction for Hydrogen Atom in Phase Space

Using elements of symmetry, as gauge invariance, several aspects of a Schrödinger equation represented in phase-space are introduced and analyzed under physical basis. The Hydrogen atom is explored in the same context. Then we add a Hénon-Heiles potential to the Hydrogen atom in order to explore chaotic features.

Muon transfer from muonic hydrogen to atomic oxygen

The muon transfer probabilities between muonic hydrogen and an oxygen atom are calculated in a constrained geometry one dimensional model for collision between 10^-6 and 10^3 eV. These estimated rates are discussed in the light of previous model calculations and available experimental data for this process.

The Hydrogen Atom as an Entangled Electron-Proton System

We illustrate the description of correlated subsystems by studying the simple two-body Hydrogen atom. We study the entanglement of the electron and proton coordinates in the exact analytical solution. This entanglement, which we quantify in the framework of the density matrix formalism, describes correlations in the electron-proton motion.

WKB-approach for the 1D hydrogen atom

Taking into account results of WKB-approximation, we derive exact quantum energies and wave functions of even and odd states in the one-dimensional Coulomb potential

Electronic Structure of Superheavy Atoms. Revisited

The electronic structure of an atom with Z <= 137 can be described by the Dirac equation with the Coulomb field of a point charge Ze. It was believed that the Dirac equation with Z > 137 is inconsistent and physically meaningless because the formula for the lower energy level of the Dirac Hamiltonian formally gives imaginary eigenvalues. But a strict mathematical consideration shows that difficulties with the electronic spectrum for Z > 137 do not arise if the Dirac Hamiltonian is correctly defined as a self-adjoint operator, see [1]. In this article, we brie y summarize the main physical resu…

Interference of Hydrogen Atom 2P(1/2) State in a Field of a Few Small Perturbations

The interference of hydrogen atom 2P(1/2) state in a field of a few small overlapping perturbations is considered in view of further applications to experimental data interpretation. On a basis of this model two new experiments are proposed which can clarify some features of Sokolov effect.

恒定磁场中二维氢原子的精确解研究

On the exact solutions of a two-dimensional hydrogen atom in a constant magnetic field

本研究针对恒定磁场中二维氢原子的精确多项式解展开，将其与瑞利-里兹法的数值结果对比，为这类已有研究的解赋予合理意义。

The Hydrogen Atom within a pseudo-complex Quantum Mechanics, involving a minimal length

The hydrogen atom is investigated, within a pseudo-complex extension of the coordinates and momenta, which introduces a minimal length scale (l) and results into a non-commutative Quantum Mechanics. After resuming the pseudo-complex extension of Quantum Mechanics, the modified energies of the hydrogen atom are deduced, producing corrections of the order of the square of the minimal length scale. Using the Lamb Shift, we obtain an upper boundary for the minimal length scale l, orders of magnitude more restrictive than former estimations.

Corrections to the ns-levels of hydrogen atom in deformed space with minimal length

We investigated the hydrogen atom problem with deformed Heisenberg algebra leading to the existence of minimal length. Using modified perturbation theory developed in our previous work [M. M. Stetsko and V. M. Tkachuk, Phys. Rev. A 74, 012101 (2006)] we calculated the corrections to the arbitrary s-levels for hydrogen atom. We received a simple relation for the estimation of minimal length. We also compared the estimation of minimal length obtained here with the results obtained in the preceding investigations.

Multigrid solution of a path integral formulation for the hydrogen atom

An efficient multigrid Monte-Carlo algorithm for calculating the ground state of the hydrogen atom using path integral is presented. The algorithm uses a unigrid approach. The action integral near r=0 is modified so that the correct values of observables are obtained. It is demonstrated that the critical slow down (CSD) is eliminated. Finally, the algorithm is compared to the staging algorithm.

Comment on 'Fisher information for quasi-one-dimensional hydrogen atom'

A further argument is provided in the discussion on the correct form of the bound-state momentum wave function of the quasi-one-dimensional hydrogen atom; namely, considering its behavior at the large quantum indices, it is reconfirmed that the complex expression from Olendski (2017) {\it Eur. J. Phys.} {\bf 38} 038001 is a correct one. Groundlessness of other interpretations is also highlighted.

Coherent states for the hydrogen atom: discrete and continuous spectra

We construct the systems of generalised coherent states for the discrete and continuous spectra of the hydrogen atom. These systems are expressed in elementary functions and are invariant under the $SO(3, 2)$ (discrete spectrum) and $SO(4, 1)$ (continuous spectrum) subgroups of the dynamical symmetry group $SO(4, 2)$ of the hydrogen atom. Both systems of coherent states are particular cases of the kernel of integral operator which interwines irreducible representations of the $SO(4, 2)$ group.

The hydrogen atom in electric and magnetic fields : Pauli's 1926 article

The results obtained by Pauli, in his 1926 article on the hydrogen atom, made essential use of the dynamical so(4) symmetry of the bound states. Pauli used this symmetry to compute the perturbed energy levels of an hydrogen atom in a uniform electric field (Stark effect) and in uniform electric and magnetic fields. Although the experimental check of the single Stark effect on the hydrogen atom has been studied experimentally, Pauli's results in mixed fields have been studied only for Rydberg states of rubidium atoms in crossedfields and lithium atoms in parallel fields.

On the N-dimensional hydrogen atom in momentum representation

We derive the wave function for N-dimensional hydrogen atom in the momentum representation with the phase factor using the generating function method and Hankel's integral.

Hydrogen atom in rotationally invariant noncommutative space

We consider the noncommutative algebra which is rotationally invariant. The hydrogen atom is studied in a rotationally invariant noncommutative space. We find the corrections to the energy levels of the hydrogen atom up to the second order in the parameter of noncommutativity. The upper bound of the parameter of noncommutativity is estimated on the basis of the experimental results for 1s-2s transition frequency.

The hydrogen atom in $D=3-2ε$ dimensions

The nonrelativistic hydrogen atom in $D=3-2ε$ dimensions is the reference system for perturbative schemes used in dimensionally regularized nonrelativistic effective field theories to describe hydrogen-like atoms. Solutions to the $D$-dimensional Schrödinger-Coulomb equation are given in the form of a double power series. Energies and normalization integrals are obtained numerically and also perturbatively in terms of $ε$. The utility of the series expansion is demonstrated by the calculation of the divergent expectation value $\langle (V')^2 \rangle$.

Dynamical symmetry of Dirac hydrogen atom with spin symmetry and its connection with Ginocchio's oscillator

The Dirac hydrogen atom with spin symmetry is shown has a SO(4) symmetry. The generators are derived, and the corresponding Casimir operator leads to the energy spectrum naturally. This type hydrogen atom is connected to a four-dimensional Dirac system with equal scalar and vector harmonic oscillator potential, by the Kustaanheimo-Stiefel transformation with a constraint.

Unruh Acceleration Radiation Revisited

When ground-state atoms are accelerated and the field with which they interact is in its normal vacuum state, the atoms detect Unruh radiation. We show that atoms falling into a black hole emit acceleration radiation which, under appropriate initial conditions (Boulware vacuum), has an energy spectrum which looks much like Hawking radiation. This analysis also provides insight into the Einstein principle of equivalence between acceleration and gravity. The Unruh temperature can also be obtained by using the Kubo--Martin--Schwinger (KMS) periodicity of the two-point thermal correlation function…

Anapole moment of a chiral molecule revisited

Parity violation in a chiral, four-atom molecule is discussed. Given the geometrical positions of the four atoms, we calculate the anapole moment of it. This problem was first discussed by Khriplovich and Pospelov. We give a detailed derivation for it so that it can be more accessible to wider range of scientists. We correct errors in their results and generalize their initial state to |s_{1/2}\rangle and |p_{1/2}\rangle states. We also discuss realistic candidates of the chiral molecules to which this approach can be applied.

The relations between d-dimensional isotropic oscillator and D-dimensional like-hydrogen atom

Being comparable in quantum systems makes it possible for spaces with varying dimensions to attribute each other using special conversions can attribute schrodinger equation with like-hydrogen atom potential in defined dimensions to a schrodinger equation with other certified dimensions with isotropic oscillator potential. Applying special transformation provides a relationship between different dimensions of two quantum systems. The result of the quantized isotropic oscillator can be generalized to like-hydrogen atom problem in different dimensions. The connection between coordinate spaces in…

Perturbation of the ns energy levels of the hydrogen atom in rotationally invariant noncommutative space

Noncommutative space which is rotationally invariant is considered. The hydrogen atom is studied in this space. We exactly find the leading term in the asymptotic expansion of the corrections to the $ns$ energy levels over the small parameter of noncommutativity.

Comment on "Clock Shift in High Field Magnetic Resonance of Atomic Hydrogen"

In this Comment, we reanalyze the experiments on the collision frequency shift of the b-c and a-d hyperfine transitions in three-dimensional atomic hydrogen in the presence of, respectively, a and b-state atoms. Accurate consideration of the symmetry of the spatial and spin part of the diatomic wavefunction yields the difference a_T-a_S=0.30(5) Åbetween the triplet and singlet s-wave scattering lengths of hydrogen atoms. This corrects the factor-of two error of the commented work [Phys. Rev. Lett. 101, 263003 (2008)].

A model with two quantum particles similar to the hydrogen atom

The hydrogen atom with the Coulomb interaction is one of the exactly solvable non-relativistic quantum models. Unlike many other exactly solvable models it describes a real physical object providing the formulas for energy levels and stationary state wave functions of a real hydrogen atom. In this paper we modify the model replacing the Coulomb interaction by the interaction of the proton and the electron with the classical electromagnetic field serving as an intermediary transmitting the electromagnetic interaction of these two charged quantum particles.

On the Hydrogen Atom in the Holographic Universe

We investigate the holographic bound utilizing a homogeneous, isotropic, and non-relativistic neutral hydrogen gas present in the de Sitter space. Concretely, we propose to employ de Sitter holography intertwined with quantum deformation of the hydrogen atom using the framework of quantum groups. Particularly, the $\mathcal U_q(so(4))$ quantum algebra is used to construct a finite-dimensional Hilbert space of the hydrogen atom. As a consequence of the quantum deformation of the hydrogen atom, we demonstrate that the Rydberg constant is dependent on the de Sitter radius, $L_Λ$. This feature is …