Hydrogen Atom In External Fields Research Articles

GOE-GUE-Poisson transitions in the nearest-neighbor spacing distribution of magnetoexcitons.

Recent investigations on the Hamiltonian of excitons by Schweiner et al.. [Phys. Rev. Lett. 118, 046401 (2017)]PRLTAO0031-900710.1103/PhysRevLett.118.046401 revealed that the combined presence of a cubic band structure and external fields breaks all antiunitary symmetries. The nearest-neighbor spacing distribution of magnetoexcitons can exhibit Poissonian statistics, the statistics of a Gaussian orthogonal ensemble (GOE), or a Gaussian unitary ensemble (GUE) depending on the system parameters. Hence, magnetoexcitons are an ideal system to investigate the transitions between these statistics. Here we investigate the transitions between GOE and GUE statistics and between Poissonian and GUE statistics by changing the angle of the magnetic field with respect to the crystal lattice and by changing the scaled energy known from the hydrogen atom in external fields. Comparing our results with analytical formulas for these transitions derived with random matrix theory, we obtain a very good agreement and thus confirm the Wigner surmise for the exciton system.

Classical approach in atomic physics

The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a semiclassical spectrum of hydrogen atom in crossed electric and magnetic fields, a spontaneous decay of excited states of a hydrogen atom, Gutzwiller's approach to Stark problem, long-lived excited states of a helium atom recently discovered with the help of Poincar$\acute{\mathrm{e}}$ section, inelastic transitions in slow and fast electron-atom and ion-atom collisions - is reviewed. Further, a classical representation in quantum theory is discussed. In this representation the quantum states are treating as an ensemble of classical states. This approach opens the way to an accurate description of the initial and final states in classical trajectory Monte Carlo (CTMC) method and a purely classical explanation of tunneling phenomenon. The general aspects of the structure of the semiclassical series such as renormgroup symmetry, criterion of accuracy and so on are reviewed as well. In conclusion, the relation between quantum theory, classical physics and measurement is discussed.

Quantum monodromy and its generalizations and molecular manifestations

Quantum monodromy is a non-trivial qualitative characteristic of certain non-regular lattices formed by the joint eigenvalue spectrum of mutually commuting operators. The latter are typically the Hamiltonian (energy) and the momentum operator(s) which label the eigenstates of the system. We give a brief review of known quantum systems with monodromy, which include such fundamental systems as the hydrogen atom in external fields, Fermi resonant vibrations of the CO2 molecule, and non-rigid triatomic molecules. We emphasize the correspondence between the classical Hamiltonian monodromy and its quantum analogue and discuss possible generalizations of this characteristic in classical integrable Hamiltonian dynamical systems and their quantum counterparts.

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.

Phase-space structure of a new integrable system related to hydrogen atoms in external fields

We explore the detailed topological structure of the phase-space of the recently discovered three-dimensional integrable but nonseparable Hamiltonian system with velocity dependent potential. Two three-parameter families of three-dimensional tori which foliate the phase-space are identified. The complete classification, according to their topology, of the level sets corresponding to the critical points of the energy-momentum map, is accomplished. The relationship of the three-dimensional integrable system with important physical systems of current interest, namely, the hydrogen atoms in circularly polarized (CP) fields, in crossed magnetic and electric fields and in crossed magnetic and CP fields, is discussed.

N-dimensional hydrogen atom in an external spherically symmetric field

TheN-dimensional hydrogen atom in external fields of the typeλr andλr2 is studied. We describe how Lie algebras are used to obtain RS-type perturbation expansions. We present expressions for the perturbation energy up to 4th order for arbitrary dimension and arbitrary state of the hydrogen atom. With symbolic computation, results are obtained in compact and transparent form.

Large order perturbation theory in the context of atomic and molecular physics—interdisciplinary aspects

AbstractThe paper is introduced by a description of the role of divergent series in mathematics and their particular use in quantum mechanics. It is emphasized that there is a formal similarity between divergent series in nonrelativistic quantum mechanics and those series occurring in quantum field theory. It is indicated that studies of divergent series in nonrelativistic quantum mechanics can be helpful in the verification of suminability techniques in quantum field theory. The general problems of the application of perturbation theory to the study of the hydrogen atom in external fields are discussed. It is shown how the problem of the continuous spectrum can be bypassed. Further it is shown that algebraic techniques are very useful for a transparent formulation of perturbation theory. The theory is applied to the study of the hydrogen atom in a magnetic field and in an electric field and also to the study of the hydrogen molecule ion. The results for the hydrogen atom in a magnetic field and the hydrogen molecule ion are discussed in detail and the large order behavior of perturbation terms is compared with analytic formulas. Finally the questions of the summability for the series corresponding to the quartic anharmonic oscillator and the hydrogen atom in a magnetic field are discussed. It is seen that large order perturbation theory can be built into a continued fraction representation of a divergent perturbation series. Numerical results are presented for the two perturbation series mentioned above.

Calculations of infinite series representing higher-order energy corrections for nonrelativistic hydrogen atoms in external fields

A new method is given for the evaluation of higher-order perturbation corrections to energy of the nonrelativistic hydrogen atom in an external field. The choice of a suitable basis in the Hilbert space of bound states for nonrelativistic hydrogen atom is exploited in the method. The infinite series which represents the higher-order energy correction in the Rayleigh-Schr\odinger perturbation theory may be expressed in such a basis in terms of finite series which are easily summed. As an illustrative example the summation of a few series, which are of importance for higher-order corrections to energy of the H atom in an external homogeneous magnetic field, is carried out.