A time-dependent unitary (canonical) transformation is found that maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass and imaginary frequency. The latter may be reduced to an ordinary harmonic oscillator by means of another unitary (canonical) transformation. A simple analysis of the resulting system leads to the identification of a previously unknown class of exactly solvable time-dependent oscillators. Furthermore, it is shown how one can apply these results to establish a canonical equivalence between some real and imaginary frequency oscillators. In particular it is shown that a harmonic oscillator whose frequency is constant and whose mass grows linearly in time is canonically equivalent with an oscillator whose frequency changes from being real to imaginary and vice versa repeatedly.

Quantum code words are highly entangled combinations of two-state systems. The standard assumptions of local realism lead to logical contradictions similar to those found by Bell, Kochen, and Specker, Greenberger, Horne and Zeilinger, and Mermin. The new contradictions have some noteworthy features that did not appear in the older ones.

It is shown that pseudoclassical many-particle systems allow for observable consequences of the spin degrees of freedom, in contrast to the one-particle system, where a consistent formulation of spin space density is impossible. After quantization, this density can then be directly compared to the decomposition of the Wigner operator in terms of spin matrices, in both the nonrelativistic and the relativistic context. From an expansion of the Dirac spinors in terms of large and small components it is seen that in the nonrelativistic limit the pseudoscalar, the timelike component of the axial-vector current, and the spatial components of the vector current vanish. The spatial components of the axial-vector current vanish in the pseudoclassical limit. The pseudoclassical appearance of spin is due to the spin-tensor contribution.

A number of interesting problems of quantum wires with different geometries can be studied with the help of conformal mapping. These include crossed wires, twisting wires, conductors with constrictions, and wires with a bend. Here the Helmholz equation with Dirichlet boundary condition on the surface of the wire is transformed to a Schrödinger-like equation with an energy-dependent nonseparable potential but with boundary conditions given on two straight lines. By expanding the wave function in terms of the Fourier series of one of the variables one obtains an infinite set of coupled ordinary differential equations. Only the propagating modes plus a few of the localized modes contribute significantly to the total wave function. Once the problem is solved, one can express the results in terms of the original variables using the inverse conformal mapping. As an example, the total wave function, the components of the current density, and the bound-state energy for a Γ-shaped quantum wire is calculated in detail.

It is a well-known fact that all the statistical predictions of quantum mechanics on the state of any physical system represented by a two-dimensional Hilbert space can always be duplicated by a noncontextual hidden-variables model. In this paper, I show that, in some cases, when we consider an additional independent (unentangled) two-dimensional system, the quantum description of the resulting composite system cannot be reproduced using noncontextual hidden variables. In particular, a no-hidden-variables proof is presented for two individual spin- particles preselected in an uncorrelated state |A〉⊗|B〉 and postselected in another uncorrelated state |a〉⊗|B〉, |B〉 being the same state for the second particle in both preselection and postselection.

Algebraic Hamiltonians based on the Casimir invariants of U(1) and O(2) dynamical symmetries of U(2) are used to describe the vibrational energy level spectrum of a diatomic molecule. The set of vibrational eigenstates arising from the U(1) chain remains closed under the operation of the appropriate ladder operators, whereas no such closure occurs in the case of the O(2) chain. This result is shown to be a consequence of the differing roles of the dimension of the irreducible representation of U(2), the so-called vibron number, in the two dynamical symmetry chains. A simple procedure is proposed to effect closure in the O(2) chain, as required for the eigenstates of a Morse oscillator Hamiltonian, to which the algebraic Hamiltonian based on the quadratic Casimir invariant of O(2) reduces within a coordinate representation. For each symmetry chain, application of the Holstein-Primakoff transformation leads to a set of ladder operators that act on one-dimensional harmonic oscillator eigenstates. Explicit comparison of the two dynamical symmetry chains is made with respect to the vibrational energy spectrum of the hydrogen molecule in its ground electronic state.

We propose an interesting method to reconstruct the Fock representation of a pure state or a density matrix describing the motion of a trapped atom.

We propose a test for small violations of the symmetrization postulate (SP) for microwave photons using Rydberg atoms in cavity QED. The method requires sequences of two properly prepared and manipulated atoms interacting with the cavity field in a dispersive manner. The cavity field is assumed to be prepared in a q-deformed coherent state. In the case when the SP holds, a sequence of two atoms would always be detected in the same state, but a small violation yields a nonzero probability that the second atom will be found in a different state. We make some estimates of the feasibility of the proposed experiment.

Detailed electron attachment and spectroscopic measurements are reported on ArF-excimer-laser irradiated ${\mathrm{H}}_2$. These studies indicate that previously reported efficient ${\mathrm{H}}^{\mathrm{-}}$ formation in ArF-laser irradiated ${\mathrm{H}}_2$ is due to electron attachment to high-lying Rydberg (HR) states indirectly populated by the laser irradiation. Electron attachment studies indicate a lifetime of ⩾40 ns for the electron attaching state(s). The spectroscopic studies show that vacuum ultraviolet emission due to the B${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathrm{u}}^{+}$→X${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$ transitions continues for up to ∼100 ns after the termination of the laser pulse and thus that the B state is populated by cascades from higher-lying states with longer lifetimes. The temporal profile of Lyman-α emission due to the H(n=2) to H(n=1) transitions is consistent with the production of H(n=2) states by electron attachment to HR states.

Electron affinities are evaluated for negative ions formed by the attachment of one electron to atoms with closed subshells, using relativistic many-body perturbation theory. In particular, we investigate the ${\mathrm{Ca}}^{\mathrm{-}}$, ${\mathrm{Sr}}^{\mathrm{-}}$, ${\mathrm{Ba}}^{\mathrm{-}}$, and ${\mathrm{Yb}}^{\mathrm{-}}$ ions. Starting from a model space that consists of nondegenerate valence Dirac-Hartree-Fock orbitals, we first approximate the energy of the attached electron as the lowest eigenvalue of a second-order effective Hamiltonian. Higher-order correlation corrections are calculated in the linear cluster approximation. The Breit interaction is also included in the first order. Our results are in good agreement with recent experiments and show a clear improvement over the second-order Dyson equation. Comparisons with other many-body calculations are also presented.

In two other papers [M. D. Faucher, O. K. Moune, D. Garcia, and P. Tanner, Phys. Rev. B 53, 9501 (1996); M. D. Faucher and O. K. Moune, J. Alloys Compounds (to be published)], it was shown that the introduction of the ${5\mathrm{f}}^{\mathrm{n}}$/${5\mathrm{f}}^{\mathrm{n}\mathrm{-}1}$7p (or ${4\mathrm{f}}^{\mathrm{n}}$/${4\mathrm{f}}^{\mathrm{n}\mathrm{-}1}$6p) configuration interaction eliminated large discrepancies in the crystal-field analysis of (i) ${\mathrm{U}}^{4+}$ (${5\mathrm{f}}^2$) in ${\mathrm{Cs}}_2$${\mathrm{UBr}}_6$ and ${\mathrm{Cs}}_2$${\mathrm{ZrBr}}_6$, for which the least root-mean-square deviation between experimental and calculated energy levels falls down from 241 to 56 ${\mathrm{cm}}^{\mathrm{-}1}$, and (ii) ${\mathrm{Nd}}^{3+}$ in ${\mathrm{Nd}}_2$${\mathrm{O}}_2$S, for which the discrepancy of the ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(2${)}_{11\mathrm{/}2}$ level is eliminated by the configuration interaction with the excited ${4\mathrm{f}}^2$6p configuration. The demonstration is now extended to ${\mathrm{Pr}}^{3+}$ and seems to be of general application. For ${\mathrm{LiYF}}_4$:${\mathrm{Pr}}^{3+}$ the mean deviation is divided by more than 2 by utilizing an interaction matrix including 4f6p in addition to the ground configuration ${4\mathrm{f}}^2$.

A method is developed for using large-order perturbation theory to solve the systems of coupled differential equations that result from the variational solution of the Schrödinger equation with wave functions of product form. This is a noniterative, computationally efficient way to solve self-consistent-field (SCF) equations. Possible applications include electronic structure calculations using products of functions of collective coordinates that include electron correlation, vibrational SCF calculations for coupled anharmonic oscillators with selective coupling of normal modes, and ab initio calculations of molecular vibration spectra without the Born-Oppenheimer approximation.

Rotationally resolved measurements are presented of interacting predissociating resonances in the Schumann-Runge bands of ${\mathrm{O}}_2$ that exhibit destructive quantum interference for energies between the line centers. The interacting resonances are described using a coupled line shape derived by treating simultaneously the perturbation and predissociation processes using the method of Fano [Phys. Rev. 124, 1866 (1961)].

The nodal structures of intrashell states of a three-valence-electron atom are investigated. We expand the wave function in the body frame of the three electrons and show that the effect of symmetry such as rotation, space inversion, and permutation is to impose nodal surfaces on the components of the wave function. The equilibrium configuration is deduced to be a coplanar equilateral triangle with the core at the center and the three electrons at the vertices. Three basic modes of internal oscillations have been identified and the relative energy levels of the atom are interpreted in terms of the degrees of excitations of these basic modes. Calculations are carried out using a model of three electrons moving on the surface of a sphere. Results from this r-frozen model, as well as the limited data in the literature, are used to illustrate conclusions drawn only from the symmetry consideration alone. We thus claim that the relative energy levels of intrashell states of a three-electron atom is determined less by the detailed dynamics and interactions, but more by the inherent quantum symmetry.

We have studied the influence of valence electron correlation on the total angular-momentum eigenstates emerging from the ${6\mathrm{s}}^2$${6\mathrm{p}}^2$ valence configuration of Pb and isoelectronic ions ${\mathrm{Bi}}^{+}$ and ${\mathrm{Po}}^{2+}$ using a variational quantum Monte Carlo method and relativistic pseudopotentials. The wave functions consist of a Jastrow factor and an antisymmetric orbital-dependent part which describes the states of the atom in an intermediate coupling scheme. A correlated sampling method has been used to reduce the statistical fluctuations, making it possible to obtain sufficiently precise energy differences, which are necessary for a discussion of differential correlation effects in the fine-structure splittings. It has been demonstrated that our ansatz reproduces well the results of relativistic pseudopotential and fully relativistic all-electron configuration interaction calculations.

The transition probability for the ${3\mathrm{d}}^{45}$${\mathrm{D}}_2$${\leftarrow }^5$${\mathrm{D}}_3$ magnetic-dipole transition in Ti-like Xe (${\mathrm{Xe}}^{32+}$) has been measured using an electron-beam ion trap. The unusually weak dependence of the transition energy on nuclear charge Z, and the fact that the transition wavelength remains in the 320- to 400-nm range for 54${\mathrm{s}}^{\mathrm{-}1}$, corresponding to a lifetime of 2.15(14) ms, in good agreement with the theoretical value of 2.4 ms.

The symmetric eikonal distorted wave method is extended to account for two-electron atom excitation by ion impact. In this formulation (SE2), the interaction between the projectile and each one of the two target electrons is taken into account in the initial and final wave functions by using the eikonal approximation. The active electron notion is not employed as both electrons are treated the same. When single configuration target wave functions are used, the SE2 transition matrix element can be expressed as a convolution of one-electron transition matrix elements. The theory is applied to the study of helium excitation by proton and highly-charged-ion impact. Experimental total and differential cross section data are well reproduced.

We develop theoretical cross sections for Penning detachment of ${\mathrm{H}}^{\mathrm{-}}$ from excited Li and Ca atoms for impact energies between 25 meV and 20 eV. We examine two kinds of cases: those that leave the target in its ground state and those that leave the target excited after the collision, namely, ${\mathrm{H}}^{\mathrm{-}}$+Li(3s), ${\mathrm{H}}^{\mathrm{-}}$+Li(3p), ${\mathrm{H}}^{\mathrm{-}}$+Li(3d), and ${\mathrm{H}}^{\mathrm{-}}$+Ca(${4\mathrm{s}5\mathrm{s}}^1$${\mathrm{S}}^{\mathrm{e}}$). Our results show that, in general, Penning detachment is enhanced when several decay channels are open and that the target is left preferentially in the nearest excited state.

We have calculated the probability for double ionization of helium by fast heavy-ion impact in the equivalent-photon picture. We find that the shape of differential cross sections is significantly affected by the inclusion of the electron-electron interaction in both the initial and the final channel, but is rather insensitive to the projectile charge and impact velocity.

The ${\mathrm{CO}}^{+}$ emission systems A-X and B-X have been studied using monochromatic photon excitation in the range 20–34 eV. The vibrational branching ratios (v′=4,5)/(v′=3,2) for the A-X system were found to remain essentially constant within this excitation range, while the (v′=1,2)/(v′=0) branching ratios for the B-X system show a 40% variation. These results are interpreted using quasidegenerate many-body perturbation theory in terms of non-Rydberg doubly excited resonances in CO, which rapidly autoionize to various low-lying ${\mathrm{CO}}^{+}$ states. It is suggested that some earlier observed variations in the photoionization branching ratios for the v′=0–2 levels of the ${\mathrm{CO}}^{+}$ ${\mathrm{X}}^2$${\mathrm{\Sigma }}^{+}$ have the same origin.