Excited states of two-dimensional hydrogen atom in tilted magnetic field: Quantum chaos

The aim of the current work is the research of the influence of a tilted magnetic field direction on the spectrum and the energy level spacing distribution of a two-dimensional (2D) hydrogen atom and of an exciton in GaAs/Al_0.33Ga_0.67As quantum well. It was discovered that the quantum chaos (QC) is initiated with an increasing angle α between the magnetic field direction and the normal to the atomic plane. It is characterized by the repulsion of levels leading to the eliminating of the shell structure and by changing the spectrum statistical properties. The statement about the initiation of chaos and its dominance over regular motion with increasing angle α is confirmed by the results of our calculations of the classical dynamics presented in this paper. The evolution of the spatial distribution of the square of the absolute value of the wave function at an increasing angle α was observed. The differences of calculated dependencies of energies for various excited states on the tilt angle at a wide range of the magnetic field strength were described.     

The hydrogen atom in a superstrong magnetic field

A new method for energy-level calculations of the H-atom in a superstrong magnetic field is proposed. The method is based on perturbation theory. The finite-difference technique is used to solve the resulting equations.     

微扰法计算中等强磁场中氢原子的能级

本文在考虑氢原子轨道运动磁矩与磁场之间、自旋磁矩与磁场之间和感生磁矩与外磁场之间的相互作用的基础上,根据角动量和球谐函数的性质,应用简并态微扰方法研究了在中等强磁场中氢原子的能级,给出了计算中等强磁场中氢原子的一级近似能级的方法,具体计算了23.5126≤B≤1.881728×10~4T范围内氢原子n=2的各能级的数值,结果与有关文献给出的理论计算值是相近的,表明本文所给出的方法是简单的、计算结果是正确的.     

Relativistic theory of a hydrogen atom in a superstrong magnetic field

The Dirac equation for a hydrogen atom in a static, uniform magnetic field is transformed by a modified FWT transformation into a mixed form; relativistic for perpendicular motion and semi-relativistic for parallel motion. In this way the adiabatic approximation can easily be obtained.     

Nuclear magnetic shielding of a hydrogen atom in an electric field

The nuclear magnetic screening constant of a hydrogen atom in a uniform electric field is calculated, neglecting any effect of electron spin. The screening is found to be reduced by the electric field for all directions of the applied magnetic field, the reduction being greatest if the two fields are perpendicular.     

Perturbative approach to the hydrogen atom in a strong magnetic field

We consider states of the hydrogen atom with the principal quantum number n≤3 and zero magnetic quantum number in a constant homogeneous magnetic field ?. The perturbation theory series is summed using the Borel transformation and conformal mapping of the Borel variable. Convergence of the approximate energy eigenvalues and their agreement with the corresponding existing results are observed for external fields up to n³?/?₀～5, where ?₀ is the atomic magnetic field. The possibility of restoring the asymptotic behavior of energy levels using perturbation theory coefficients is also discussed.     

High-order perturbation theory for the hydrogen atom in a magnetic field

The states of a hydrogen atom with principal quantum numbers n⩽3 in a constant uniform magnetic field ℋ are studied. Coefficients in the expansion of the energy of these states in powers of ℋ² up to the 75th order are obtained. Series for the energies of the states and the wave functions are summed to values of ℋ on the order of the atomic magnetic field. A generalization of the moment method upon which these calculations are based can be used in other cases in which a hydrogen atom is perturbed by a potential with a polynomial dependence on the coordinates. Zh. éksp. Teor. Fiz. 113, 550–562 (February 1998)     

Aq-analogue of a two-dimensional hydrogen atom

A new method for theq-analogue of a hydrogen atom is presented. By using the method, we construct a model of a two-dimensionalq-hydrogen atom, and determine its energy, angular momentum, and state vectors. The method may be extended to cases of arbitrary dimension.     

On the spectrum of the hydrogen atom in an ultrastrong magnetic field

Various approaches to computing the energies of the ground state and excited levels of the hydrogen atom in an ultrastrong magnetic field B that considerably exceeds the field B _a = m _e ² e ³ c/ħ ³ ∼ 10⁹ G are considered. The effects of polarization of vacuum and anomalous magnetic moment of the electron on the position of the atomic levels are discussed. The vacuum polarization effects are negligibly weak for B < 10¹⁵ G but become significant in fields B ≫ 10¹⁶ G, in which these effects qualitatively modify the atomic spectrum in this range. The difference in the behaviors of the even and odd energy levels for B ≫ B _a is analyzed and the formulas for the energies of odd levels as a function of field B are refined.     

A hydrogen atom in a superstrong magnetic field and the Zeldovich effect

We consider the problem of a hydrogen atom in a superstrong magnetic field, B? B _a =2.35×10⁹ G. The analytical formulas that describe the energy spectrum of this atom are derived for states with various quantum numbers n_ρ and m. A comparison with available calculations shows their high accuracy for B?B _a . We note that the derived formulas point to a manifestation of the Zeldovich effect, i.e., a rearrangement of the atomic spectrum under the influence of strong short-range Coulomb potential distortion. We discuss the relativistic corrections to level energies, which increase in importance with magnetic field and become significant for B?10¹⁴ G. We suggest the parameters in terms of which the Zeldovich effect has the simplest form. Analysis of our precision numerical calculations of the energy spectrum for a hydrogen atom in a constant magnetic field indicates that the Zeldovich effect is observed in the spectrum of atomic levels for superstrong fields, B?5×10¹¹ G. Magnetic fields of such strength exist in neutron stars and, possibly, in magnetic white dwarfs. We set lower limits for the fields B_min required for the manifestation of this effect. We discuss some of the properties of atomic states in a superstrong magnetic field, including their mean radii and quadrupole moments. We calculated the probabilities of electric dipole transitions between odd atomic levels and a deep ground level.     

Adiabatic representation for a hydrogen atom photoionization in a uniform magnetic field

A new effective method of calculating wave functions of discrete and continuous spectra of a hydrogen atom in a strong magnetic field is developed on the basis of the adiabatic approach to parametric eigenvalue problems in spherical coordinates. The two-dimensional spectral problem for the Schrödinger equation at a fixed magnetic quantum number and parity is reduced to a spectral parametric problem for a one-dimensional angular equation and a finite set of ordinary second-order radial differential equations. The results are in good agreement with the photoionization calculations by other authors and have a true threshold behavior.     

二维氢原子的相对论修正

求解了二维氢原子的狄拉克方程,得到了精确的相对论能级与波函数,并详细讨论了非相对论极限.     

Anisotropic states of two-dimensional electrons in high magnetic fields

We study the collective states formed by two-dimensional electrons in Landau levels of index n > or = near half filling. By numerically solving the self-consistent Hartree-Fock (HF) equations for a set of oblique two-dimensional lattices, we find that the stripe state is an anisotropic Wigner crystal (AWC), and determine its precise structure for varying values of the filling factor. Calculating the elastic energy, we find that the shear modulus of the AWC is small but finite (nonzero) within the HF approximation. This implies, in particular, that the long-wavelength magnetophonon mode in the stripe state vanishes q(3/2) like as in an ordinary Wigner crystal, and not like q(5/2) as was found in previous studies where the energy of shear deformations was neglected.     

Energy spectrum of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field of arbitrary strength

We compute, via a variational mixed-base method, the energy spectrum of a two-dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the non-relativistic and spinless case. We find that the relativistic spectrum does not present s states.     

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

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

The hydrogen atom in strong magnetic fields: Summation of the weak field series expansion

Using the weak field expansion, we have calculated the ground-state energy of the hydrogen atom in a magnetic field for values of the field up to about 10¹³G. The perturbative expansion has been summed by an order-dependent mapping method. We compare our results with previous calculations. Our method allows us to obtain: first, more accurate values of the binding energy for a field up to 10¹⁰G, then good results in the transition region between the two sets of accurate calculations of the literature, and finally still reasonably accurate values up to 10¹³G.     

强磁场中氢原子的能级结构

发展了一套简单高效的非微扰理论方法研究强磁场中的原子能级结构.作为例子,给出了磁场强度从0到1000个原子单位,氢原子基态和低激发态的结合能以及四极矩等重要原子能级结构参数.结果表明:相对于其他的高精度计算方法,该方法不仅能计算出高精度的能级位置而且可方便给出精确的电子波函数.此外,该法还具有很强的普适性,可直接推广到原子与任意方向的交叉电磁场相互作用的研究. 关键词： 强磁场 CWDVR谱方法 氢原子能级结构 四极矩