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The ability to manipulate single atoms has opened up the door to constructing interesting and useful quantum structures from the ground up. On the one hand, nanoscale arrangements of magnetic atoms are at the heart of future quantum computing and spintronic devices; on the other hand, they can be used as fundamental building blocks for the realization of textbook many-body quantum models, illustrating key concepts such as quantum phase transitions, topological order or frustration. Step-by-step assembly promises an interesting handle on the emergence of quantum collective behavior as one goes from one, to few, to many constituents. To achieve this, one must however maintain the ability to tune and measure local properties as the system size increases. Here, we use low-temperature scanning tunneling microscopy to construct arrays of magnetic atoms on a surface, designed to behave like spin-1/2 XXZ Heisenberg chains in a transverse field, for which a quantum phase transition from an antiferromagnetic to a paramagnetic phase is predicted in the thermodynamic limit. Site-resolved measurements on these finite size realizations reveal a number of sudden ground state changes when the field approaches the critical value, each corresponding to a new domain wall entering the chains. We observe that these state crossings become closer for longer chains, indicating the onset of critical behavior. Our results present opportunities for further studies on quantum behavior of many-body systems, as a function of their size and structural complexity., published online on 18 Apr 2016 in Nature Physics

A discussion is carried on about how to characterize quantum mechanically chemical bonds within a molecular structure. Molecular atom- and atom pair-bond operators are constructed. Afterwards an atom and bond expectation values (A-BEV) matrix defined using expectation values of these operators. It is furthermore discussed how one can consider the complete sum of the A-BEV matrix as a collective quantum mechanical descriptor of the atoms and bonds attached to a molecular structure.

Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The calculation has been extended to all transitions between p and s states having main quantum numbers not exceeding 6. An evident similarity between the intensity pattern obtained from the Joule-Lenz law and the corresponding quantum-mechanical transition pro-babilities has been shown.

The interaction between two two-level atoms via photon exchange is simulated. The language of qubits is used with the aim of possible application of this model to the construction of quantum processors based on the interaction of several atoms with unit photons. The study involves a qubit form of the Jaynes-Cummings-Hubbard model with two-photon excitations and its polariton modification, in which any displacement of photons between cavities is associated with a photon absorbed or emitted by an atom. Relaxation is described by the Kossakowski-Lindblad equation for the density matrix of electron and photon states. The relaxation time is obtained as a function of the photon transition probability between atoms and of the amplitude of the photon interaction with an atom. Additionally, the degree of agreement between the density matrices in both models is calculated. An artifact of incomplete relaxation is described in the case of fuzzy qubit semantics, when the description of photons depends on their number.

John L. Heilbron describes the route that led Niels Bohr to quantize electron orbits a century ago.

The question of whether hydrogen atoms can exist or not in spaces with a number of dimensions greater than 3 is revisited, considering higher dimensional Euclidean spaces. Previous results which lead to different answers to this question are briefly reviewed. The scenario where not only the kinematical term of Schr\"odinger equation is generalized to a D-dimensional space but also the electric charge conservation law (expressed here by the Poisson law) should actually remains valid is assumed. In this case, the potential energy in the Schr\"odinger equation goes like 1/r^{D-2}. The lowest quantum mechanical bound states and the corresponding wave functions are determined by applying the Numerov numerical method to solve Schr\"odinger's eigenvalue equation. States for different angular momentum quantum number (l = 0; 1) and dimensionality (5 \leq D \leq 10) are considered. One is lead to the result that hydrogen atoms in higher dimensions could actually exist. For the same range of the dimensionality D, the energy eigenvalues and wave functions are determined for l = 1. The most probable distance between the electron and the nucleus are then computed as a function of D showing the possibility of tiny bound states., Comment: 19 pages, 6 figures

Most spin squeezed states are realized in cold atom systems containing relatively small number of atoms. However, in quantum limited metrology, the signal is proportional to atom number N while the noise is proportional to √N. The signal noise ratio (SNR) increases as atom number increases.

A scheme of high-precision two- and three-dimensional (3D) atom localization is proposed and analyzed by using a density matrix method for a five-level atom-light coupling scheme. In this system four strong laser components (which could be standing waves) couple a pair of atomic internal states to another pair of states in all possible ways to form a closed-loop diamond-shape configuration of the atom-light interaction. By systematically solving the density matrix equations of the motion, we show that the imaginary part of the susceptibility for the weak probe field is position dependent. As a result, one can obtain information about the position of the atom by measuring the resulting absorption spectra. Focusing on the signatures of the relative phase of the applied fields stemming from the closed- loop structure of the diamond- shape subsystem, we find out that there exists a significant phase dependence of the eigenvalues required to have a maximum in the probe absorption spectra. It is found that by properly selecting the controlling parameters of the system, a nearly perfect 2D atom localization can be obtained. Finally, we numerically explore the phase control of 3D atom localization for the present scheme and show the possibility to obtain 1/2 detecting probability of finding the atom at a particular volume in 3D space within one period of standing waves.

We consider two two-level atoms fixed at different positions, driven by a resonant monochromatic laser field, and interacting collectively with the quantum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics of the two atoms and the steady-state is obtained analytically for a configuration of the atoms. The steady-state populations of the energy levels of the free atoms, entanglement, quantum and geometric discords and degree of mixedness are calculated analytically as a function of the laser field intensity and the distance between the two atoms. It is found that there is a possibility of considerable steady-state entanglement and left/right quantum discord and that these can be controlled either by increasing/decreasing the intensity of the laser field or by increasing/decreasing the distance between atoms. It is shown that the system of two atoms can be prepared in a separable mixed state with non-zero quantum discord that turns into an $X$-state for high laser field intensities. The behavior and relationships between the different correlations are studied and several limiting cases are investigated.

The purpose of this work is to show the stability of the hydrogen atom with the use the Quantum Oscillatory Modulated Potential and the Heisenberg equations of motion, postulating that the electron in the hydrogen atom is behaving as a quantum harmonic oscillator. With the electron confined between two potential barriers, created by the new potential function, we are considering that at absolute temperature the power absorbed or emitted by the electron per unit of time can be used to determine the zero point energy of the oscillator. Assuming that electron is only exchanging energy with the nucleus of the atom we are making use of the operators of creation and annihilation of a photon to explain how the energy between the proton and the electron can be exchanged to keep the atom a stable system.

We make use of the Quantum Theory of Atoms in Molecules (QTAM) to partition the total energy of a many-electron system into intra- and interatomic terms, by explicitly computing both the one- and two-electron contributions. While the general scheme is formally equivalent to that by Bader et al., we focus on the separation and computation of the atomic self-energies and all the interaction terms. The partition is ultimately performed within the density matrices, in analogy with McWeeny's Theory of Electronic Separability, and then carried onto the energy. It is intimately linked with the atomistic picture of the chemical bond, not only allowing the separation of different two-body contributions (point-charge-like, multipolar, total Coulomb, exchange, correlation, ...) to the interaction between a pair of atoms but also including an effective many-body contribution to the binding (self-energy, formally one-body) due to the deformation of the atoms within the many-electron system as compared to the free atoms. Many qualitative ideas about the chemical bond can be quantified using this scheme.

We define a quantum spectrum function using the eigenvalues and the eigenfunctions in the system of two-dimensional artificial atom. We find that the Fourier transform of the quantum spectrum function reveals a lot of information of the classical closed orbits and the classical opened orbits from one point to another. These results give new evidence about the classical-quantum correspondence.

The quantum theory of atoms in molecules (QTAIM) is generalized to include relativistic effects using the popular scalar-relativistic zeroth-order regular approximation (SR-ZORA). It is usually assumed that the definition of the atom as a volume bounded by a zero-flux surface of the electron density is closely linked to the form of the kinetic energy, so it is somewhat surprising that the atoms corresponding to the relativistic kinetic-energy operator in the SR-ZORA Hamiltonian are also bounded by zero-flux surfaces. The SR-ZORA Hamiltonian should be sufficient for qualitative descriptions of molecular electronic structure across the periodic table, which suggests that QTAIM-based analysis can be useful for molecules and solids containing heavy atoms.

Information theoretic atomic properties within the quantum theory of atoms in molecules (QTAIM) are discussed. The fate of the dimensions of the electron density inserted into the logarithm of Shannon’s entropy is examined. It is shown that referencing the atomic missing information function to the corresponding uniform electron gas captures most of the size-dependence and converts the non-transferable atomic missing information into a transferable property. A striking trend relates an atom’s contribution to the overall Coulombic correlation energy and that atom’s Shannon’s entropy. The information theoretic atomic properties obtained from MP2, DFT, or Hartree–Fock (H–F) are almost perfectly correlated.

The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.

Quantum scattering of photons inside a one-dimensional waveguide caused by a number of closely located resonant two-level atoms is studied using the theory of integrable quantum systems. The multi-particle wave function of scattered photons is represented as a sum of terms of different degrees of “entanglement.” For two-photon scattering we discuss explicitly differences in photon correlations for the single two-level atom case and the case of several atoms.

Owing to the degeneracy of the energy levels, the wavefunction of the electron in the excited states of the hydrogen atom and hydrogen-like ions perturbed by a neutral atom B is significantly different from the wavefunction of the unperturbed state. The perturbed function has a wide high maximum in the region of atom B, which is explained by multiple collisions of the electron with atom B, because the classical trajectories in the Coulomb field are closed and the size of atom B is much smaller than the size of the excited-state orbit. The radiative lifetimes of the excited states are much larger than those of unperturbed states. The orbital angular momentum L of the excited electron is strongly changed in collisions with atom B owing to the quantum interference or mixing of the temporal phases of adiabatic wavefunctions. The cross sections for such a change in the orbital angular momentum are several orders of magnitude larger than the cross sections found in early investigations in the approximation of the single collision of the electron with atom B.

An explicit classification of consistent variational constraints within the context of the "quantum theory of proper open subsystems" as well as the "quantum theory of atoms in molecules" (QTAIM) it presented. It is demonstrated that the general variational procedure is not sensitive enough to discriminate between different mathematically consistent variational conditions. The uniqueness of the regional kinetic energy is employed to derive the net zero-flux condition and the regions satisfying this condition are named as quantum divided basins. A modified form of the local zero-flux is proposed in order to define topological atoms within the context of the orthodox QTAIM. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem 109: 726 -732, 2009

In this contribution some basic problems of practical applications of quantum mechanics to the functioning of microsystems have been discussed. In particular, it has been shown that starting from fundamental principles one cannot calculate 3D-cinfigurations of atoms in molecules. In order to get meaningful results in these calculations, the empirical information about the configuration of molecule is necessary. The problem of variables separation in quantum chemistry was discussed. It has been shown that the separation of electronic and

The quantum correlation between a pair of photons, emitted by a Δ- type atom, is calculated. The correlation show anti-bunching property, and the second correlation function is dependent on classical field Ω. So we can control the magnitude of the joint detection probability by adjusting the driving field. In addition, Δ-type atom can also work as storage and retrieving apparatus.

This paper demonstrates that it is straightforward to develop the theory of an atom in a molecule--the extension of quantum mechanics to an open system--by deriving the necessary equations of motion from Schrödinger's equation, followed by a comparison of the predicted properties with experiment to determine the correct boundary condition. Although less fundamental than the variational derivation of the quantum theory of atoms in molecules, this heuristic approach makes the quantum mechanics of an atom in a molecule accessible to "everyman" possessing a knowledge of Schrödinger's equation, aiding its general acceptance by experimental chemists.

Asingle neutral atom trapped by light is a promising qubit. It has weak, well-understood interactions with the environment, its internal state can be precisely manipulated1, interactions that entangle atoms can be varied from negligible to strong2,3,4 and many single atoms can be trapped near each other in an optical lattice5. This collection of features would allow for a relatively large quantum computer6 if each neutral atom qubit could be independently detected and addressed7,8,9,10. A quantum computer with even 50 qubits would allow quantum simulations that are out of the reach of classical computers11,12. So far, fewer than ten single atoms have been simultaneously imaged13. Here we demonstrate trapping and imaging of 250 single atoms in a three-dimensional optical lattice and show that imaging is highly unlikely to change the pattern of site occupancy. Our lattice spacing is large enough that, in principle, individual atoms can be addressed, which in combination with reproducible imaging should allow for verifiable filling of vacancies, execution of site-specific quantum gates and measurement of each atom’s final quantum state14,15. The lattice we use can readily be scaled to include thousands of trapped atoms.

We merge in this Letter electron number distribution functions at the coarse-grained level provided by the quantum theory of atoms in molecules and the interacting quantum atoms approach. We show that, together, they provide an appealing chemical image of how the spatial localization and the statistical dependence of electrons translate into the energetic features of simple bonds. This is done in the lowest singlet and triplet states of H2.

We represent the deterministic substitute of the Schrodinger equation for a hydrogen atom in precise accordance with the Bohm-de Broglie interpretation of quantum mechanics. To construct a mathematical model, the Weierstrass theorem and limit cycles are used. This method can be applied to many-electron atoms.

An accurate system-bath model to investigate the quantum dynamics of hydrogen atoms chemisorbed on graphene is presented. The system comprises a hydrogen atom and the carbon atom from graphene that forms the covalent bond, and it is described by a previously developed 4D potential energy surface based on density functional theory ab initio data. The bath describes the rest of the carbon lattice and is obtained from an empirical force field through inversion of a classical equilibrium correlation function describing the hydrogen motion. By construction, model building easily accommodates improvements coming from the use of higher level electronic structure theory for the system. Further, it is well suited to a determination of the system-environment coupling by means of ab initio molecular dynamics. This paper details the system-bath modeling and shows its application to the quantum dynamics of vibrational relaxation of a chemisorbed hydrogen atom, which is here investigated at T = 0 K with the help of the multi-configuration time-dependent Hartree method. Paper II deals with the sticking dynamics.

If the reader is already familiar with quantum mechanics he may just want to browse this chapter and return later if necessary. However, readers who have experienced quantum mechanics up to now only as compulsory mathematical exercise may perhaps read this chapter with advantage and find it helpful to approach the indispensable instruments without big formal hurdles. In Sects. 2.1–2.3 we summarize a minimum of formalism. Section 2.4 treats as a first example the well known particle in a box and the free electron gas which in atomic and solid state physics is an important elementary model. Section 2.5 gives an overview of how to treat angular momenta, needed in all following text, specified in Sect. 2.5.4 for the electron spin s=1/2. Section 2.6 offers a ‘crash course’ in nonrelativistic quantum mechanics of the H atom – essential knowledge for all the following chapters. We refrain here from formal derivations in favour of a plausible, possibly somewhat hand waving introduction. Finally, Sect. 2.7 presents a first, elementary approach to interactions of atomic electrons with external fields, which will be extended and deepened in Chap. 8. Clearly, such a brief introduction into quantum mechanics cannot substitute a profound study of the formal theory. It should, however, facilitate the access to it and make the reader ‘fit’ for the following chapters.

In this paper, we briefly summarize the new information which have been deduced on the atom–atom interaction from cold atom experiments. These information are quite unusual and very interesting. Their interpretation is considerably simplified if high quality quantum chemistry calculations are available. After an overview of the domain, we discuss in detail the experiments performed with metastable helium atom, thus showing the variety of new data obtained in this case and the importance of quantum chemistry calculations for their interpretation.

We show in this paper that the electron’s quantum dynamics in hydrogen atom can be modeled exactly by quantum Hamilton–Jacobi formalism. It is found that the quantizations of energy, angular momentum, and the action variable ∫p dq are all originated from the electron’s complex motion, and that the shell structure observed in hydrogen atom is indeed originated from the structure of the complex quantum potential, from which the quantum forces acting upon the electron can be uniquely determined, the stability of atomic configuration can be justified, and the electron’s complex trajectories can be derived accordingly. Based on the derived electron’s trajectory, we can explain why the electron appears at some positions with large probability, while at some other positions with small probability. The positions with maximum probability predicted by standard quantum mechanics are found to be just the stable equilibrium points of the electron’s non-linear complex dynamics. The electron’s trajectories in hydrogen atom are discovered to be very diverse and strongly state-dependent; some of them are open and non-periodic, while some are closed and periodic. Over such a great diversity of orbits, commensurability condition ensuring the existence of closed orbit will be derived and the de Broglie’s standing wave pattern will be identified. Along the investigation of the electron’s orbits in hydrogen atom, we will also clarify why old quantum mechanics using the concept of classical orbit can correctly predict the energy quantization of hydrogen atom and meanwhile why it is not applicable to general quantum system. Finally, the internal mechanism of how the precessing, non-conical eigen-trajectories can evolve continuously to the classical, non-precessing, conical orbits as n → ∞ is explained in detail.

An experimentalist approaching theory for an understanding of conceptual chemistry that can be related to measurable properties, focuses on the electron density distribution. One finds in the topology of the electron density the definition of an atom, of the bonding between atoms, and of the boundary condition for the extension of quantum mechanics to an open system – to an atom in a molecule. This paper describes this approach, as it evolved from the failure of existing models to a study of molecular charge distributions and of how these studies resulted in the extension of quantum mechanics to an open system using the action principle.

A method to compute two-electron integrals over arbitrary regions of space is introduced and particularized to the basins appearing in the quantum theory of atoms in molecules. The procedure generalizes the conventional multipolar approach to account for overlapping densities. We show that the approach is always convergent and computationally efficient, scaling as N(4) in the worst, two-center case. Several numerical results supporting our claims are also presented.

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.

Basic electromagnetism and relativistic quantum theory are used to evaluate the magnetic field due to the electron in a one-electron atom. The field patterns are displayed and discussed for several eigenstates with low values of the quantum numbers. The effect of increasing the number of protons in the nucleus is shown explicitly. Comparison with the non-relativistic result illustrates the effects of relativity in atoms. There is a brief discussion of the meaning of the terms spin and orbital magnetic moment of an atom in the light of these results.

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180° out of phase with the initial state.

Contracted Gaussian-type function sets are developed for correlating p, d, and f functions for a valence electron of the hydrogen atom and alkali-metal atoms from Li to Rb. A segmented contraction scheme is used for its compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from the K orbitals of the atoms. The present basis sets yield an accuracy comparable to the correlation-consistent basis set for the hydrogen atom and also give a similar high accuracy for the alkali-metal atoms. In the calculations of spectroscopic constants of alkali hydrides, the decontraction of the p function plays an important role, especially for LiH. The contributions of d and f functions are nontrivial for KH and RbH.

Wave functions for one-electron diatomic molecules such as H2+ and HeH2+ are analyzed by Bader’s atoms in molecules method. The locations of the degenerate axial critical points in the electron density generated from sigma states arising from the n=1–6 united atom manifolds are shown to correspond well with the boundaries of domains obtained solely from a classical description of the electron motion. The relationship clarifies the connection between the atomic and molecular regimes of classical trajectories and the quantum description of the states. In particular, the classical transition from atomic to molecular character roughly corresponds to the appearance of a critical point in the electron density located on the internuclear axis between the nuclei. The global aspects of the relationship between the classical and quantum descriptions helps to demonstrate the classical framework of the quantum picture.

Quantum correlations between two neighbor atoms are studied. It is assumed that one atomic system comprises a single auto-ionizing level and the other atom does not contain any auto-ionizing level. The excitation of both atoms is achieved by the interaction with the same mode of the quantized field. It is shown that the long-time behavior of two atoms exhibits quantum correlations even when the atoms do not interact directly. This can be shown using the optical excitation of the neighbor atom. Also a measure of entanglement of two atoms can be applied after reduction of the continuum to two levels., 11 pages, 21 figures

The concepts of atoms and bonds in molecules which appeared in chemistry during the nineteenth century are unavoidable to explain the structure and the reactivity of the matter at a chemical level of understanding. Although they can be criticized from a strict reductionist point of view, because neither atoms nor bonds are observable in the sense of quantum mechanics, the topological and statistical interpretative approaches of quantum chemistry (quantum theory of atoms in molecules, electron localization function and maximum probability domain) provide consistent definitions which accommodate chemistry and quantum mechanics.

We study quantum inversion of a cold atom in the Jaynes-Cummings model when its centre-of-mass (CM) motion is described quantum mechanically. The atom and the quantized cavity mode are initially prepared in the excited state and the coherent state, respectively. Many dramatic changes take place in atomic inversion when the atomic CM motion experiences a transition from the classical regime to the quantum regime. For ultra-cold atoms, in particular, fine resonances are found in the inversion. This novel effect, which originates from the de Broglie wave character of the atomic CM motion, is a direct manifestation of the `granularity' of the high-intensity cavity field. By means of the atom-field dressed-state picture, we explain the related phenomena in a qualitative way.

We discuss experimental results on Stern-Gerlachinterferometry with atoms. After a theoretical approachsuited for fast atoms, we discuss elementary experimentson the preservation of atomic coherence. Then we examine the action of theinterferometer as producing atoms with new properties,beaded atoms, and their radiative properties.

It is shown that the number of dynamical variables (computer storage) which is necessary for a description is similar for the coupled quantum-classical description and for the pure quantum one. In the Schrodinger representation, the dynamic equations of the coupled quantum-classical description are shown to be nonlinear in terms of the wave function and incompatible with the quantum axiomatics. As a result, the quantum-classical description appears to be impossible in the Heisenberg representation, because it uses essentially the quantum axiomatics, which is incompatible with the quantum-classical description. An idea of a description, intermediate between the purely quantum description and the classical one, is suggested. In this case, the number of dynamic variables (computer storage) is several times as large as the classical description, but it is much less than at the pure quantum description. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 483–498, 1999

The standard Quantum Mechanics is statistical in nature and cannot provide a detailed picture of an atom. The Deterministic Theory of Atomic Structure, derived from a system of equations that govern the electrodynamics in atoms, can account for the stability of the atoms. We describe the chirality of an atom, the rules for forming molecules, and the assemblies of the superconducting material from Aluminum and Silicon.

We present the general quantum theory for the micromaser with ultra-cold Λ-type three-level atoms. We first derive the dressed states for the interaction of a Λ-type three-level atom with a quantum cavity field, then treat the interaction between the injection atom with the cavity field as a scattering process, find the reflection and transmission coefficients in this process, and calculate the atomic emission probability.

The multipole expansion of the electron - nucleus interaction in the so-called high-frequency limit of the Floquet theory in the Kramers - Henneberger frame is used to determine equivalent point-charge distributions. This allows the use of standard quantum chemistry programs to calculate the energies. It is found that satisfactory results can be obtained with a quadrupole approximation if the parameter (, amplitude of electric field; , frequency of the field) does not exceed 30 au. The examples which are treated are the hydrogen atom, the hydrogen negative ion and the hydrogen molecular ion , systems for which accurate results are available.

It is shown that in atom optics physical systems arise which have close similarities to quantum group structures. A particular example for which an atomic operator provides a representation of the quantum group GLq(2,C) forq=−1 is presented.