We consider the theoretical problem of finding the bound eigenstates of an infinite nonuniform two-dimensional waveguide with Dirichlet boundary conditions. Using a coordinate transformation we show that this is equivalent to finding the eigenstates of a uniform waveguide with a potential proportional to the eigenvalue. Hence there is a sense in which the bound states occurring in nonuniform waveguides are analogous to bound states due to potentials in uniform waveguides.

This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum-mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are discussed, and used to show that the quantum-mechanical version of the classical transformation does not leave the measure of the path-integral invariant, instead inducing an anomaly. The relation to operator techniques and ordering problems is discussed, and special attention is paid to incorporation of the initial and final states of the transition element into the boundary conditions of the problem. Classical canonical transformations are developed to render an arbitrary power potential cyclic. The resulting Hamiltonian is analyzed as a quantum system to show its relation to known quantum-mechanical results. A perturbative argument is used to suppress ordering-related terms in the transformed Hamiltonian in the event that the classical canonical transformation leads to a nonquadratic cyclic Hamiltonian. The associated anomalies are analyzed to yield general methods to evaluate the path integral’s prefactor for such systems. The methods are applied to several systems, including linear and quadratic potentials, the velocity-dependent potential, and the time-dependent harmonic oscillator.

Size consistency of the Brillouin-Wigner perturbation theory is studied using the Lippmann-Schwinger equation and an exponential ansatz for the wave function. Relation of this theory to the coupled cluster method is studied and a comparison through the effective Hamiltonian method is also provided.

Joint position-momentum observables are defined to be covariant POV measures on the group ${\mathit{openR}}^3$×${\mathit{openR}}^3$^ of space translations and boosts. For elementary or finite quantum systems, it is shown that there is no covariant PV measure on ${\mathit{openR}}^3$×${\mathit{openR}}^3$^ into the von Neumann algebra generated by average position and momentum. So these cannot be measured sharply at the same time. For an infinite quantum system, we construct a covariant PV measure on ${\mathit{openR}}^3$×${\mathit{openR}}^3$^ into the von Neumann algebra generated by average position and momentum. Therefore average position and momentum of an infinite quantum system can be measured sharply at the same time.

The motion of a particle along a one-dimensional closed curve in a plane is considered. The only restriction on the shape of the loop is that it must be invariant under a twofold rotation about an axis perpendicular to the plane of motion. Along the curve a symmetric double-well potential is present leading to a twofold degeneracy of the classical ground state. In quantum mechanics, this degeneracy is lifted: the energies of the ground state and the first excited state are separated from each other by a slight difference ΔE, the tunnel splitting. Although a magnetic field perpendicular to the plane of the loop does not influence the classical motion of the charged particle, the quantum-mechanical separation of levels turns out to be a function of its strength B. The dependence of ΔE on the field B is oscillatory: for specific discrete values ${\mathit{B}}_{\mathit{n}}$ the splitting drops to zero, indicating a twofold degeneracy of the ground state. This result is obtained within the path-integral formulation of quantum mechanics; in particular, the semiclassical instanton method is used. The origin of the quenched splitting is intuitively obvious: it is due to the fact that the configuration space of the system is not simply connected, thus allowing for destructive interference of quantum-mechanical amplitudes. From an abstract point of view this phenomenon can be traced back to the existence of a topological term in the Lagrangian and a nonsimply connected configuration space. In principle, it should be possible to observe the splitting in appropriately fabricated mesoscopic rings consisting of normally conducting metal.

A purely dynamical explanation for the quantum Zeno effect is proposed. It is argued that a quantum system undergoes a quantum-Zeno-type dynamics as a consequence of a particular type of evolution involving a series of frequent spectral decompositions. The role of quantum measurements and of the ‘‘collapse of the wave function’’ is investigated and it is clarified that, provided a final observation is performed, the dynamical quantum Zeno effect can be obtained without making use of von Neumann’s projection postulate. The meaning of infinitely frequent measurements is critically discussed and it is argued that it should be regarded as a mathematical idealization, impossible to realize from a physical point of view.

A Taylor-series expansion of the density functional F[n] is constructed from the given expansion for the energy E[v]. The formalism is used to investigate the noninteracting kinetic-energy functional for one-dimensional systems. Furthermore, a formal analysis of the Taylor expansion of the density functional for an interacting electron system at finite temperature is given and the relation between density-functional theory and the field-theoretical approach to the many-particle problem is enlightened.

The responses of hydrogenic states of highly excited Rydberg atoms to dc and rf electric fields have been studied and the data interpreted from both classical and quantal viewpoints. The solution of the Schrödinger equation for this system leads to a network of progenitor and sideband states, a Floquet-Stark map that, although complex, exhibits regularities. These regularities are interpreted from a classical viewpoint by considering the near-Keplerian orbit of the valence electron as the dynamical entity rather than the electron itself. It is shown that the regularities in the Floquet-Stark map are the result of a commensurability of the dc Stark frequency and that of the applied rf. The experimental technique employed, Floquet spectroscopy, also provides data from which atomic parameters may be extracted, in this case the quantum of the (permanent) electric dipole moment (QDM) associated with hydrogenic manifolds of sodium Rydberg atoms. It is observed that the QDM’s for sodium are larger than those for corresponding states of hydrogen. This observation is interpreted from a classical point of view.

Multichannel quantum-defect theory is applied to the gerade n=2 and 3 states of ${\mathrm{H}}_2$. In the first paper in this series [Phys. Rev. A 49, 4353 (1994)] we obtained the quantum-defect matrix of the strongly interacting ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$ double-minimum states of ${\mathrm{H}}_2$ by fitting to the ab initio clamped-nuclei electronic energies of Wolniewicz and Dressler. This matrix was used in the second paper [Phys. Rev. A 49, 4364 (1994)] to calculate the N=0 vibronic energies of the corresponding electronic states. In this paper we calculate the N≥0 rovibronic energies of the singlet and triplet gerade n=2 and 3 states of ${\mathrm{H}}_2$. This ab initio treatment accounts for both singly and doubly excited channels and reproduces the rovibronic energies with almost the same accuracy as the more traditional coupled-equations approach. Additionally, the experimental singlet-triplet splittings for the f levels, and the evolution of these splittings with vibrational and rotational quantum numbers, are reproduced very well.

The previously derived approximation for an atom in time-dependent electric fields [P. Krstić and Y. Hahn, Phys. Rev. A 48, 4515 (1993)] is improved for electric pulses of both short and long duration. The transitions that involve a distorted continuum are studied in detail, and the phenomenon of momentum coherence is shown to greatly enhance the transition amplitudes. A detailed comparison with the recent experiment of Jones, You, and Bucksbaum [Phys. Rev. Lett. 70, 1236 (1993)] is presented, where a half-cycle high-power laser pulse was used to ionize Rydberg atoms.

Hyperfine structure of the 5${\mathit{d}}^3$6${\mathit{s}}^2$ ${}_{}{}^4{}_{}{}^{}$${\mathit{F}}_{3/2}$ ground state in ${}_{}{}^{180\mathit{m}}{}_{}{}^{}\mathrm{Ta}$ i was precisely measured by means of atomic-beam laser-rf double-resonance spectroscopy. Hyperfine-interaction constants A and B for the ground state ${}_{}{}^4{}_{}{}^{}$${\mathit{F}}_{3/2}$ were determined with accuracies of 3 and 10 ppm, respectively. The nuclear electric quadrupole moment was derived, as well as a precise value of the magnetic moment for ${}_{}{}^{180\mathit{m}}{}_{}{}^{}\mathrm{Ta}$ (${\mathit{I}}^{\mathrm{\pi }}$=$9^{\mathrm{-}}$): the magnetic dipole moment is ${\mathrm{\mu }}_{\mathit{I}}^{180\mathit{m}}$=+4.825(11)${\mathrm{\mu }}_{\mathit{N}}$ and the spectroscopic quadrupole moment is ${\mathit{Q}}_{\mathit{s}}^{180\mathit{m}}$=+4.946(20)b.

The performance of a recently proposed ab initio description of chemisorption problems, obtained by reducing the total many-body Hamiltonian to a superposition of bond-pair Hamiltonians, is tested. This scheme, which in its Hartree-Fock version leads to an independent-particle model of the tight-binding form, is applied to analyze the interaction curves for the hydrides of the first-row elements as a function of internuclear distances. By fixing the occupation numbers for the orthonormal spin orbitals at large internuclear separations, its relationship with results from both the valence-bond and the molecular-orbital methods is established. It is shown that the model works fairly well in predicting binding energies, equilibrium distances, dipole moments, and vibrational frequencies for the whole series of the hydrides. It was also found that if a consistent expansion of the intervening parameters is made up to second order in the atomic-orbital overlaps, reasonable results are obtained for the hydrides forming bonds of nearly ionic character: LiH, OH, and FH.

A general equation is constructed for the magneto-optical spectra of the forward-scattered light observed through an analyzer when an absorption cell in a homogeneous magnetic field is illuminated by a linearly polarized laser beam at an arbitrary angle to the field direction. The Faraday effect and the Voigt effect are deduced as special solutions of this general equation. For the case of Voigt geometry, π-polarized light whose plane of polarization is parallel to the applied magnetic field gives a simple absorption profile. σ-polarized light oscillating perpendicularly to the static magnetic field contains an interference term between right and left circularly polarized light as well as absorption terms. For these eigenwaves (π,σ) for the Voigt effect, the spectral shapes are independent of the angle of the analyzer, only their intensity is modified by the angle. For the general case, experimental results for cesium vapor and theoretical spectra show good agreement.

A measurement of the Stark-induced amplitudes α and β for the 6${\mathit{P}}_{1/2}$→7${\mathit{P}}_{1/2}$ transition in atomic thallium is reported. Absorption of cw laser light tuned to this transition at 293 nm was compared to absorption of 378-nm cw laser light tuned to the allowed 6${\mathit{P}}_{1/2}$→7${\mathit{S}}_{1/2}$ transition. The absorption sample was an intense atomic beam in the presence of a strong electric field. The measured values are α=2.01(4)×${10}^{\mathrm{-}5}$ ${\mathrm{\mu }}_{\mathit{B}}$/ (V/cm) and β=1.67(4)×${10}^{\mathrm{-}5}$${\mathrm{\mu }}_{\mathit{B}}$/ (V/cm), where ${\mathrm{\mu }}_{\mathit{B}}$ is the Bohr magneton. These results are in agreement with semiempirical theory, but disagree with previous measurements of these amplitudes in this laboratory. A critical analysis of the previous measurement is given to explain the discrepancy. The newly measured value of β makes it necessary to reinterpret previous measurements of parity nonconservation in the 6${\mathit{P}}_{1/2}$→7${\mathit{P}}_{1/2}$ transition. In the course of the present experiment, Stark shifts of the 6${\mathit{P}}_{1/2}$→7${\mathit{P}}_{1/2}$ and 6${\mathit{P}}_{1/2}$→7${\mathit{S}}_{1/2}$ transitions were also measured: Δν(6${\mathit{P}}_{1/2}$→7${\mathit{S}}_{1/2}$)=-112(6) kHz/(kV/cm${)}^2$ and Δν(6${\mathit{P}}_{1/2}$→7${\mathit{P}}_{1/2}$)=-618(31) kHz/(kV/cm${)}^2$. These results are also in good agrement with semiempirical theory.

We present a relativistic many-body calculation of the 2${\mathit{s}}_{1/2}$ and 2${\mathit{p}}_{1/2,3/2}$ ionization energies in Li-like ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, based on the coupled-cluster singles and doubles approximation with the inclusion of the unretarded Breit interaction, using Dirac-Fock-Breit orbitals. A detailed comparison is made with a similar calculation using ordinary Dirac-Fock orbitals. The calculation yields the transition energies, and by comparison with the recently published experimental values we find the value for the remaining quantum-electrodynamical correction, which is compared with recent Lamb-shift calculations. The importance of an accurate nuclear model for evaluating the nuclear-size effect is also discussed.

The Schrödinger equation for atomic hydrogen in a large electric field F is solved by separation in parabolic coordinates. As F→∞, the scaled field f that enters the separated equations tends to 0. Thus the large-F asymptotics depend on the small-f behavior of the separated equations, each of which in turn is equivalent to a quarticly perturbed two-dimensional anharmonic oscillator. The Bender-Wu branch cuts of the oscillator play a major role in the hydrogen asymptotics. A simple iterative algorithm permits the calculation of the branch points at which two eigenvalues coincide. We have found numerically that, as F→∞, the separation constant ${\mathrm{\beta }}_1$ returns to the smaller of the unperturbed values ${\mathrm{\beta }}_1^{\mathrm{}\left(0\right)\mathrm{}}$ or ${\mathrm{\beta }}_2^{\mathrm{}\left(0\right)\mathrm{}}$. At the same time, ${\mathrm{\beta }}_2$ tends to the negative of the smaller value. As the real electric field F increases from 0 to ∞, in each case that ${\mathrm{\beta }}_1^{\mathrm{}\left(0\right)\mathrm{}}$ and ${\mathrm{\beta }}_2^{\mathrm{}\left(0\right)\mathrm{}}$ are not equal, the trajectory of either f or ${\mathit{e}}^{\mathrm{-}\mathit{i}\mathrm{\pi }}$f (but not both) loops around a single branch point and passes through the cut that joins the two (${\mathrm{\beta }}_1^{\mathrm{}\left(0\right)\mathrm{}}$ and ${\mathrm{\beta }}_2^{\mathrm{}\left(0\right)\mathrm{}}$) Riemann triple sheets. All other branch cuts are avoided. No branch cuts are crossed if ${\mathrm{\beta }}_1^{\mathrm{}\left(0\right)\mathrm{}}$=${\mathrm{\beta }}_2^{\mathrm{}\left(0\right)\mathrm{}}$. The known small-f asymptotic expansion for the discontinuity of the separation constant, in the f plane, across the negative real axis leads to a large-F asymptotic expansion for E in terms of the parabolic quantum numbers ${\mathit{n}}_1$, ${\mathit{n}}_2$, and m.

The (e,2e) triple differential cross section and generalized oscillator strengths of the helium atom ionization with simultaneous excitation have been calculated for the kinematic arrangements of the recent measurements and calculations of Dupré et al. [J. Phys. B 25, 259 (1992)]. The first Born calculation has been performed with an initial correlated multiconfiguration Hartree-Fock helium atom ground state and a coupled-channel final state of the ion and ejected ‘‘slow’’ electron. We find generally good agreement with the experiment, which is a substantial improvement on the previous calculations.

One of the principal advantages of electron momentum spectroscopy (EMS) is that peaks in the binding-energy spectrum can be assigned with greater certainty than in photoelectron spectroscopy, through a comparison of the EMS triple-differential cross sections with the theoretically calculated spherically averaged momentum distributions (MD’s) of Dyson orbitals. While the target Hartree-Fock approximation is commonly used to calculate the Dyson orbital MD’s for this purpose, a computationally less demanding method would allow the advantages of EMS to be extended to larger molecules. This paper considers the use of Kohn-Sham density-functional theory for this purpose. Although Dyson orbitals are not among the quantities that can be calculated exactly (in the limit of the exact exchange-correlation functional) within the framework of Kohn-Sham density-functional theory, the Kohn-Sham equation can be regarded as an approximate form of Dyson’s quasiparticle equation, with a local self-energy. The well known shortcomings of this approach for estimating ionization potentials and band gaps do not a priori imply a corresponding problem with the orbitals. After discussing these formal considerations, we introduce the ‘‘target Kohn-Sham approximation’’ as a means of approximating Dyson orbitals by Kohn-Sham orbitals. The quality of this approximation for the calculation of MD’s is assessed by comparison with high-quality configuration-interaction calculations, the target Hartree-Fock approximation, and experiment, for several small molecules. The quality of the target Kohn-Sham approximation MD’s is found to be comparable to that of the MD’s from the target Hartree-Fock approximation, with evident practical implications for EMS.

We have measured the magnetic dipole (M1) and electric quadrupole (E2) amplitudes in the D1 transition of rubidium atoms placed in a static electric field, ${\mathit{scrE}\to }_{\mathit{s}}$. The interference of the Stark induced M1 and E2 amplitudes with the normal E1 amplitude gives the atomic absorptivity a linear dependence on ${\mathit{scrE}\to }_{\mathit{s}}$ and on the atomic spin polarization. We find that the fractional change in absorptivity due to the Stark interference is ${\mathit{a}}_{\mathit{M}1}$+${\mathit{a}}_{\mathit{E}2}$=(-2.37±0.37±0.28)×${10}^{\mathrm{-}8}$ (kV/cm${)}^{\mathrm{-}1}$.

Relativistic correlation energies have been computed for the neutral rare-gas atoms Ne, Ar, Kr, Xe, and Rn, the group-IIB atoms Zn, Cd, and Hg, and the ions of the Ne isoelectronic sequence with up to Z=100 by means of a recently developed relativistic many-body perturbation theory based on the no-pair Dirac-Coulomb-Breit Hamiltonian. Analytic basis sets of Gaussian-type functions are employed to expand the upper and lower components of the Dirac four-spinors in the matrix Dirac-Fock self-consistent-field and relativistic many-body perturbation procedures. The effects of the low-frequency Breit interaction on relativistic many-body effects for high-Z neutral atoms and Ne-like highly ionized ions are examined.