A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ)=${\sum }_{\mathrm{\ell }}$${\mathrm{U}}^{\left(\mathrm{\ell }\right)}$(τ) with ${\mathrm{U}}^{\left(\mathrm{\ell }\right)}$(τ) being at least of the order ${\nu }^{\mathrm{\ell }}$. In particular, ${\mathrm{U}}^{\mathrm{}\left(0\right)\mathrm{}}$(τ) corresponds to the adiabatic approximation and yields Berry's adiabatic phase. It is shown that this series expansion has nothing to do with the 1/τ expansion of U(τ). It is also shown that the nonadiabatic part of the evolution operator is generated by a transformed Hamiltonian which is off-diagonal in the eigenbasis of the initial Hamiltonian. This suggests the introduction of an adiabatic product expansion for U(τ) which turns out to yield exact expressions for U(τ) for a large number of quantum systems. In particular, a simple application of the adiabatic product expansion is used to show that for the Hamiltonian describing the dynamics of a magnetic dipole in an arbitrarily changing magnetic field, there exists another Hamiltonian with the same eigenvectors for which the Schrödinger equation is exactly solvable. Some related issues concerning geometric phases and their physical significance are also discussed.

We consider a driven damped anharmonic oscillator that classically leads to a bistable steady state and to hysteresis. The quantum counterpart for this system has an exact analytical solution in the steady state that does not display any bistability or hysteresis. We use quantum-state diffusion theory to describe this system and to provide a new perspective on the lack of hysteresis in the quantum regime so as to study in detail the quantum to classical transition. The analysis is also relevant to measurements of a single periodically driven electron in a Penning trap where hysteresis has been observed.

The form factor for the transition between the hydrogenic states with parabolic quantum numbers ${\mathrm{n}}_1$${\mathrm{n}}_2$m and ${\mathrm{n}}_1^{|\mathrm{I}\mathrm{H}}$${\mathrm{n}}_2^{|\mathrm{I}\mathrm{H}}$${\mathrm{m}}^{|\mathrm{I}\mathrm{H}}$ is obtained in a closed analytic form. The asymptotic limit of the transition form factor at large parabolic quantum numbers is derived, and a comparison with exact quantum calculations shows that the asymptotic limit is accurate in a wide region of parabolic quantum numbers and the momentum p transferred to electrons. A simple quasiclassical formula for the transition probability is given, and the range of quantum numbers corresponding to quasiclassically forbidden transitions are defined.

We describe a method to perform a single quantum measurement of an arbitrary motional observable of a single ion moving in a harmonic potential. We illustrate the measurement procedure with explicit examples, namely the position and phase observables. A necessary tool for this is the ability to synthesize an arbitrary motional state. In addition, we show how to generalize this to higher dimensions, and show explicit examples of how to engineer states in two spatial dimensions, including a proposed experimental configuration.

The concept of distance in Hilbert space is relevant in a variety of scenarios, in particular for investigating the quality of different approximations. In this work we study the relations between (i) statistical distances (SD) on a probability space, on the one hand, and (ii) different metrics on Hilbert space (MHS), on the other hand. As a result, we are able to establish some universal relations between SD and MHS and to apply them to one-dimensional problems.

The consistent histories formulation of the quantum theory of a closed system with a pure initial state defines an infinite number of incompatible consistent sets, each of which gives a possible description of the physics. We investigate the possibility of using the properties of the Schmidt decomposition to define an algorithm which selects a single, physically natural, consistent set. We explain the problems which arise, set out some possible algorithms, and explain their properties with the aid of simple models. Though the discussion is framed in the language of the consistent histories approach, it is intended to highlight the difficulty in making any interpretation of quantum theory based on decoherence into a mathematically precise theory.

Certain multiparticle Bell inequalities, which involve measurements of collective observables, can be violated by quantum mechanics to a proportionately greater extent than the conventional two-particle Bell-Clauser-Horne-Shimony-Holt inequality. We give examples of such inequalities and show how their potential for enhanced violation can be attributed to the nonlocal character of the observables.

We show that dynamical localization for excited hydrogen atoms in magnetic and microwave fields takes place at quite low microwave frequency (ω${\mathrm{n}}^3$≪1). Estimates of the localization length are given for different parameter regimes, showing that the quantum delocalization border drops significantly as compared to the case of zero magnetic field. This opens up broad possibilities for laboratory investigations.

A radial magnetic field can induce a time-invariance-violating electric-dipole moment (EDM) in quantum systems. The EDMs of the Tl, Cs, Xe, and Hg atoms and the neutron that are produced by such a field are estimated. The contributions of such a field to the constants, χ of the T, P-odd interactions ${\mathrm{\chi }}_{\mathrm{e}}$N⋅s/s and ${\mathrm{\chi }}_{\mathrm{N}}$N⋅I/I are also estimated for the TlF, HgF, and YbF molecules [where s (I) is the electron (nuclear) spin and N is the molecular axis]. The best limit on the contact monopole field can be obtained from the measured value of the Tl EDM. The possibility of such a field being produced from polarization of the vacuum of electrically charged magnetic monopoles (dyons) by a Coulomb field is discussed, as well as the limit on these dyons. An alternative mechanism involves chromomagnetic and chromoelectric fields in QCD.

Applying closed-orbit theory to the recurrence spectra of the hydrogen atom in a magnetic field, one can interpret most, but not all, structures semiclassically in terms of closed classical orbits. In particular, conventional closed-orbit theory fails near bifurcations of orbits where semiclassical amplitudes exhibit unphysical divergences. Here we analyze the role of ghost orbits living in complex phase space. The ghosts can explain resonance structures in the spectra of the hydrogen atom in a magnetic field at positions where no real orbits exist. For three different types of catastrophes, viz. fold, cusp, and butterfly catastrophes, we construct uniform semiclassical approximations and demonstrate that these solutions are completely determined by classical parameters of the real orbits and complex ghosts.

Relativistic effects in the binding energy, the bond length, and vibrational frequencies of ground-state potential-energy curves are investigated for ${\mathrm{Tl}}_2$,${\mathrm{Pb}}_2$, and ${\mathrm{Bi}}_2$ by performing relativistic and nonrelativistic all-electron Dirac-Fock-Slater ${\mathrm{X}}_{\mathrm{\alpha }}$ calculations. Wave functions from numerical solutions of Dirac(Hartree)-Fock-Slater equations for atoms are taken as basis sets. A variationally consistent approximation for the direct Coulomb potential has been used for efficiently obtaining accurate potential energy curves. Our calculations confirm that the spin-orbit effect weakens the binding of the 6p-element molecules ${\mathrm{Tl}}_2$,${\mathrm{fPb}}_2$, and ${\mathrm{Bi}}_2$.

We calculate the electronic structure of several atoms and small molecules by direct minimization of the self-interaction-corrected–local-density-approximation (SIC-LDA) functional. To do this, we first derive an expression for the gradient of this functional under the constraint that the orbitals be orthogonal and then show that previously given expressions do not correctly incorporate this constraint. In our atomic calculations, the SIC-LDA yields total energies, ionization energies, and charge densities that are superior to results obtained with the local density approximation (LDA). However, for molecules, SIC-LDA gives bond lengths and reaction energies that are inferior to those obtained from LDA. The nonlocal Beck-Lee-Yang-Parr functional, which we include as a representative generalized gradient approximation functional, outperforms both LDA and SIC-LDA for all ground-state properties we considered.

A simplification of the modified configuration-interaction (MCI) method [S. P. Goldman, Phys. Rev. A 52, 3718 (1995)] is introduced. In its original form, the MCI method improves dramatically the convergence of standard CI calculations by a modification of the radial representation and an a priori mixing of a large number of angular configurations. In this work, the large but finite number of angular configurations mixed is replaced by an infinite number of configurations. Angular integrations are performed in closed form, resulting in simpler angular momentum calculations. Numerical accuracy and stability are substantially improved as one avoids handling very large values of angular momentum quantum numbers. As a result, calculations involving very high angular mixing can be done with a much shorter amount of CPU time. This angular method can be used in the framework of CI or MCI (i.e., using standard or ordered radial electron coordinates).

A Dirac-like Hamiltonian H with two-body terms, and its no-pair Hamiltonian ${\mathrm{H}}^{+}$=${\mathrm{\Lambda }}^{++}$H${\mathrm{\Lambda }}^{++}$ where ${\mathrm{\Lambda }}^{++}$ is related to a one-particle Hamiltonian ${\mathrm{h}}_0$, are studied in finite-basis representations H and ${\mathbf{H}}^{+}$. Using finite-basis eigenfunctions of ${\mathrm{h}}_0$, it holds ${\mathrm{E}}_{\mathrm{i}}^{+}$⩽${\mathrm{E}}_{{\mathrm{N}}^{\mathrm{-}}+\mathrm{i}}$, i>0, where ${\mathrm{E}}_{{\mathrm{N}}^{\mathrm{-}}+\mathrm{i}}$ and ${\mathrm{E}}_{\mathrm{i}}^{+}$ are the ordered eigenvalues of H and ${\mathbf{H}}^{+}$, and ${\mathrm{N}}^{\mathrm{-}}$ is the difference between the dimensions of H and ${\mathbf{H}}^{+}$. The states of order i⩽${\mathrm{N}}^{\mathrm{-}}$ exhibit continuum dissolution. In contrast, those of order ${\mathrm{N}}^{\mathrm{-}}$+i, i>0, are bounded from below and after application of a variational principle they represent bound states.

The multiconfiguration Dirac-Fock method has been used to obtain the electron affinities of group-13 (IIIB) elements (B, Al, Ga, In, and Tl). Interactions among outer electrons (three for a neutral atom and four for an anion) in both ground and excited states were included in all calculations. Our calculated electron affinities for B, Al, Ga, In, and Tl are 0.260 eV, 0.433 eV, 0.305 eV, 0.393 eV, and 0.291 eV. We find that effects of exchange interaction and relativity on electron affinity are important in explaining the trend seen in the electron affinities of the elements of group 13.

For atoms or molecules, a general argument is given justifying expanding well behaved density functionals in series of functionals that are homogeneous to different degrees with respect to density scaling. Employing only appropriate local homogeneous functionals 〈${\mathrm{\rho }}^{\mathrm{k}}$〉, few-term fits of atomic Hartree-Fock T[ρ],${\mathrm{nE}}_{\mathrm{x}}$[ρ], and J[ρ] (kinetic energy, exchange energy, and classical Coulomb repulsion energy density functionals) are shown to give excellent results, as do self-consistent calculations on atoms using this ${\mathrm{E}}_{\mathrm{x}}$[ρ] plus an earlier obtained representation of ${\mathrm{E}}_{\mathrm{c}}$[ρ]. The representations may be local (as the one for ${\mathrm{E}}_{\mathrm{c}}$) or nonlocal, where nonlocal products of two or more 〈${\mathrm{\rho }}^{\mathrm{k}}$〉 can be included.

Generalized oscillator strengths for the vibronic bands of ${\mathrm{A}}^1$Π, ${\mathrm{B}}^1$${\mathrm{\Sigma }}^{+}$, ${\mathrm{C}}^1$${\mathrm{\Sigma }}^{+}$, and ${\mathrm{E}}^1$Π have been determined by an angle-resolved electron energy loss spectroscopy at an incident electron energy of 1500 eV and in an angular range of 0.5°–6.0°. The corresponding absolute optical oscillator strengths obtained by extrapolating the generalized oscillator strengths to ${\mathrm{K}}^2$=0 are also reported. The present results have been compared with previous work, and some differences between them have been explained. The experimental generalized oscillator strengths for ${\mathrm{v}}^{|\mathrm{I}\mathrm{H}}$=0–8 of ${\mathrm{A}}^1$Π, ${\mathrm{v}}^{|\mathrm{I}\mathrm{H}}$=0–1 of ${\mathrm{B}}^1$${\mathrm{\Sigma }}^{+}$, ${\mathrm{C}}^1$${\mathrm{\Sigma }}^{+}$, and ${\mathrm{E}}^1$Π are reported.

A detailed spectroscopic study of resonant states in the continuum of lithiumlike carbon has been performed utilizing dielectronic recombination at an ion storage ring. All observed resonances have been identified and energies have been determined with an accuracy better than 0.1 eV. The measurements have been complemented by accurate calculations using the saddle-point technique. Every resonance of the type ${1\mathrm{s}\mathrm{n}\mathrm{l}\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$${\mathrm{l}}^{|\mathrm{I}\mathrm{H}}$ has been determined for n=2, ${\mathrm{n}}^{|\mathrm{I}\mathrm{H}}$=2,3).

The formulas of Fromm and Hill and of Remiddi, for the three-electron correlated atomic integral using Slater-type atomic orbitals, are shown to be equivalent in their common region of applicability. The demonstration required the derivation of an identity connecting dilogarithm functions which is either new or not widely known. It is then shown how to modify the more general of these formulas (that of Fromm and Hill) to eliminate the necessity of branch tracking in the complex plane and thereby to achieve a straightforwardly computable formalism. By obtaining a formal cancellation of the individual-term singularities in the Fromm-Hill formula, problems of numerical instability are also avoided. The work is validated with a computer program and sample calculations.

Kr spectra from 300 nm to 460 nm produced in an electron-beam ion trap (EBIT) are reported in this work. The spectra include magnetic dipole (M1) transitions from Kr XXIII and Kr XXII, as well as electric dipole (E1) lines of Kr II and Kr III. Two new capabilities of the EBIT at the National Institute of Standards and Technology, time resolved data acquisition and extracted ion analysis, are used to aid in the charge state identification.