The effect of a random perturbation is investigated for a Hamiltonian with systematic degeneracies. It turns out that the influence of the degeneracies remains significant under a perturbation. In particular, the eigenvectors manifest specific patterns when the perturbation produces all characteristics of quantum chaos for the spectrum.

Spatial correlations between electromagnetic fields arising from neutral sources with electric-dipole transition moments are calculated using nonrelativistic quantum electrodynamics in the multipolar formalism. Expressions for electric-electric, magnetic-magnetic, and electric-magnetic correlation functions at two points r and r’ are given for a source molecule in either a ground or an excited state. In contrast to the electric-electric and magnetic-magnetic cases there are no electric-magnetic correlations for a ground-state molecule. For an excited molecule the downward transitions contribute additional terms which have modulating factors depending on (r-r’)/λ/. From these correlation functions electric and magnetic energy densities are found by setting r=r’. These energy densities are then used in a response formalism to calculate intermolecular energy shifts. In the case of two ground-state molecules this leads to the Casimir-Polder potential. However, for a pair of molecules, one or both excited, there are additional terms arising from downward transitions. An important feature of these energies is that they exhibit an ${\mathit{R}}^{\mathrm{-}2}$ dependence for large intermolecular separations R. This dependence is interpreted in terms of the Poynting vector, which itself can be obtained by setting r=r’ in the electric-magnetic correlation function.

An expansion in powers of ${\mathrm{ħ}}^2$ is developed for the integral over all angles of an arbitrary smooth function times the cross section for a particle scattering from a time-independent potential. An explicit expression is given for the leading quantum correction, which is illustrated with the example of scattering in two dimensions from a 1/${\mathit{r}}^2$ potential.

An isomorphism is realized between the (q)-deformed harmonic oscillator and a particular anharmonic oscillator model: it permits insight into the problem of the physics behind the deformation parameter q. In our model, the anharmonic coupling strength is shown to be proportional to q. The isomorphism permits us also to analyze and to interpret the appearance of various nonclassical features induced by a q deformation during the time evoluton of an su(2) coherent state.

We devise and apply a method for the calculation of the exact propagator for the Schrödinger equation for the one-dimensional Hamiltonian scrH(p,x)=${\mathit{p}}^2$/2m+${\mathit{V}}_0$Θ(x). The limiting cases ${\mathit{V}}_0$→0 (free particle) and ${\mathit{V}}_0$→∞ (opaque wall) are checked. The method is also applicable to any piecewise-constant potential.

We expound the generalized covariance condition in quantization. This condition is combined with the other standard conditions to determine the quantum-mechanical operator of a quadratic Hamiltonian ${\mathit{H}}_2$, represented by a quadratic function of momenta with a nonsingular coefficient matrix depending on coordinates, and the operator of an arbitrary quadratic quantity ${\mathit{F}}_2$ belonging to a system whose Hamiltonian is of the ${\mathit{H}}_2$ type. It is shown that the operator of ${\mathit{F}}_2$ depends also on ${\mathit{H}}_2$ and that H${\mathrm{^}}_2$ or F${\mathrm{^}}_2$ cannot contain a curvature term. We also present a modified ordering method with certain conditions under which the operator of a quadratic quantity can be found by replacing some linear functions of momenta with their operators. Finally, a path-integration formula is formed and shown to yield the expression of H${\mathrm{^}}_2$ that we derive by the canonical quantization method.

We evaluate the exact (Pancharatnam) phase differences between the final state ‖ψ(t)〉 and various initial states for a spin-1/2 particle in a rotating magnetic field B(t). For initial states ‖n;${\mathbf{B}}_{\mathrm{ef}}$(0)〉, which are eigenstates of the spin component along the direction of the initial effective field ${\mathbf{B}}_{\mathrm{ef}}$(0), the exact phase has an energy-dependent part and an energy-independent part. It is shown that these states ‖n;${\mathbf{B}}_{\mathrm{ef}}$(0)〉 are cyclic and their corresponding Aharonov-Anandan phases are evaluated. In the adiabatic limit we discuss different choices of time-dependent bases and the relationship between the exact phase, the Born-Fock-Schiff phase, and Berry’s phase. We propose neutron interference experiments to test separately the exact and the adiabatic evolution laws, as well as to measure exact and adiabatic time-dependent phases.

Classical and quantum models of a localized spin driven by a polarized-spin beam have been shown to exhibit a rich variety of dynamical behaviors. In the classical model these include stable limit points, limit cycles, and chaos; however, in the quantum model the density matrix of the localized spin generally approaches a steady state. This paradox is resolved by considering the autocorrelation functions of the spin components, which reveal the expected quantum-classical correspondence. The noncommuting of the limits j→∞ and t→∞ is explained in this model by the limiting behavior of certain eigenvalue distributions, and the significance of these limits is discussed. The study also highlights the unresolved problem of interpreting the complex correlation functions of noncommuting operators.

The eigenvalues of a quantum system depending on two parameters become degenerate at isolated points in the parameter space, which are called diabolical points because of their double-cone structure. Varying one parameter produces near-degeneracies termed avoided crossings. Some results on the density of these objects in parameter space can be obtained by requiring consistency with the level repulsion exhibited by the distribution of energy-level spacings. The density of diabolical points and the distribution of their ellipticities are obtained exactly for the Gaussian orthogonal ensemble random-matrix model. The distribution of their separations in parameter space is also investigated.

The most accurate measurements of the electron g factor involve the observation of spin flips of a single electron trapped in a magnetic field and having a cyclotron quantum number very near the ground state. This paper examines the excitation of these flips, finding the following results: The spin-flip rate and the observed shape of the anomaly resonance can be substantially altered when the quantum nature of the cyclotron motion is taken into account. Excitation by rf magnetic field gradient, while in principle the preferable method, may not be feasible at liquid-helium temperatures due to slow transition rates. Excitation by driven oscillations in a static magnetic field gradient is accompanied by several frequency shifts which have not been very important to date but which are likely to significantly affect future measurements.

We have developed perturbative expressions for the energies of high-angular-momentum Rydberg states of halogen and inert-gas isoelectronic sequences. These expressions allow us to determine polar- izabilities and estimate susceptibilities of the cores. They also provide simple expressions for the quantum defects.

The observed nonmonotonic behavior of the atomic electron momentum density of neon and some members of its isoelectronic sequence at the Hartree-Fock level is investigated. Further evidence is provided by showing that the nonmonotonicity observed for the neon series at the Hartree-Fock level is still present when a cusp condition and the correct asymptotic behavior are imposed onto the Hartree-Fock wave function. This result is also observed for the results obtained from highly correlated configuration-interaction wave functions. Furthermore, we substantiate the argument that the observed nonmonotonicities are most probably due to higher-order terms in the ${\mathit{Z}}^{\mathrm{-}1}$ perturbation theory.

Doubly excited or Feshbach-type resonant states in heliumlike systems, Z=2–10, have been calculated using the complex-rotation method. Using Hylleraas-type wave functions having up to 825 terms, we predict resonance parameters (both resonance positions and widths) below the N=3, 4, and 5 thresholds of the hydrogenic systems. The present results for Z=7 and 8 are compared with those of the close-coupling calculations and experimental results where available.

The trajectories of the highly excited hydrogen atom with nonvanishing pseudomomentum K are investigated. As a characteristic feature, we observe the intermittent behavior of the internal as well as of the center-of-mass motions which consist of alternating phases of strongly chaotic and quasiregular motion. During these phases, interesting physical phenomena appear. These phenomena as well as the intermittent behavior of the trajectories can be explained by the observation that, due to the finite nuclear mass, an additional confining potential appears. This confining potential has strong impact on the ionization of the hydrogen atom in general. We also investigate the correlation between the values of the internal angular momentum ${\mathit{L}}_{\mathit{z}}$ and the internal coordinate ρ. In fact, we are able to control intermittency by choosing different values of the energy, pseudomomentum, and magnetic-field strength.

The two-photon-annihilation contribution to the positronium hyperfine interval is obtained in analytic form at order m${\mathrm{\alpha }}^6$ using the Fried-Yennie gauge. The contribution to the hyperfine interval is -0.0325m${\mathrm{\alpha }}^6$=-0.606 MHz. This differs from the result of an earlier Feynman gauge evaluation. The errors in the earlier calculation are identified. The corrected Feynman gauge result agrees with the Fried-Yennie gauge result.

A general scheme of qualitative analysis is applied to molecular rovibrational problems. The classical-quantum correspondence provides a description of different classes of localized quantum rotation-vibration states associated with localized classical motion. A description of qualitative features, such as localized motion, and of qualitative changes, such as localization phenomena, is based on the concept of the simplest Hamiltonian. It uses only the topological properties of the compact reduced phase space and the action of the symmetry group on this space. The qualitative changes of the simplest Hamiltonian are analyzed as bifurcations caused by rotational or vibrational excitation. The relation between the stationary points of the classical Hamiltonian function on the reduced phase space and the principal periodic trajectories in the coordinate space is analyzed for vibrational Hamiltonians. In particular, the relation between the nonlinear normal modes, proposed by Montaldi, Roberts, and Stewart [Philos. Trans. R. Soc. London, Ser. A 325, 237 (1988)], and normal- and local-mode models widely used in molecular physics is discussed. Along with a general consideration of localized rotational and vibrational states a more detailed analysis of the vibrational dynamics of an $X_3$ molecule with the $D_{3h}$ symmetry, such as the ${\mathrm{H}}_3^{+}$ molecular ion, is given.

The atomic quadrupole moments ${\mathit{Q}}_{\mathit{z}\mathit{z}}$ of Be(2s2p${;}^3$${\mathit{P}}_2$), Al(3p${;}^2$${\mathit{P}}_{3/2}$), In(5p${;}^2$${\mathit{P}}_{3/2}$), Ne(2${\mathit{p}}^5$3${\mathit{s}}^3$${\mathit{P}}_2$), Ar(3${\mathit{p}}^5$4s${;}^3$${\mathit{P}}_2$), Kr(4${\mathit{p}}^5$5s${;}^3$${\mathit{P}}_2$), and Xe(5${\mathit{p}}^5$6s${;}^3$${\mathit{P}}_2$) have been calculated using a finite-element multiconfiguration Hartree-Fock method. The obtained ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(Be) of 2.265 a.u. agrees with previously calculated values. The calculated ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(Al) and ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(In) of 2.579 and 3.165 a.u. are in good agreement with the experimental values of 2.53(15) a.u. and 2.94(10) a.u. A large s-d polarization contribution to the ${\mathit{Q}}_{\mathit{z}\mathit{z}}$ of the rare gases is found in the present calculations. The correlation contributions from double (D), triple (T), and quadruple (Q) excitations to the ${\mathit{Q}}_{\mathit{z}\mathit{z}}$ of the rare gases alternate; the total DTQ correlation contribution is negligibly small for Ne, Ar, and Kr, while the DTQ correlation contribution to the ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(Xe) is 25% of the final ${\mathit{Q}}_{\mathit{z}\mathit{z}}$. The final values are ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(Ne)=-0.0506 a.u., ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(Ar)=-0.0553 a.u., ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(Kr)=+0.0601 a.u., and ${\mathit{Q}}_{\mathit{z}\mathit{z}}$(Xe)=+0.4505 a.u., as compared to the experimental values of -0.048(5) a.u., -0.042(4) a.u., +0.046(5) a.u., and +0.30(3) a.u. for Ne, Ar, Kr, and Xe, respectively.

A model for the density-functional-theory (DFT) softness kernel is proposed. The model satisfies a number of known physical conditions such as translational invariance, the Hellmann-Feynman theorem, and the correct normalization of the linear-response function for a system with a constant number of electrons. Henceforth, explicit formulas are obtained for a number of DFT reactivity parameters. Our procedure is applied to derive a rather simple and compact formula to compute atomic static dipole polarizabilities α within the DFT formalism. We find α=2〈${\mathit{r}}^3$〉/Z, in atomic units where Z is the atomic number and 〈${\mathit{r}}^3$〉 is the expectation of ${\mathit{r}}^3$. This formula predicts qualitatively good values and tendencies for atoms with 4≤Z≤36. Furthermore, the associated radial induced dipole-moment density behaves as expected.

The electron correlation in some low-lying doubly excited states of the ${\mathrm{H}}_2$ molecule is investigated by analyzing two-body correlation functions in comparison with the corresponding doubly excited states of He. Effects of increasing the internuclear distance and of avoided crossings are discussed. Some interesting features of electron-correlation patterns are found to appear because of the additional symmetries of the molecule. Autoionization widths of the doubly excited states are evaluated and the autoionization mechanisms are analyzed in connection with the electron correlation.

With finite basis sets constructed from B splines, a systematical many-body perturbation calculation of the Be-like atoms with Z from 3 to 36 is performed. A two-configuration model space (2s+2p${)}^2$ is adopted in the calculation in order to speed the perturbation convergence. With perturbations up to the second order, we obtain 93–99.8 % of the total correlation energies given by Davidson et al. [Phys. Rev. A 44, 7071 (1991)] for Z from 4 to 20. The discrepancies between experimental and theoretical values approach a constant of 0.0005 while atomic number Z increases.