The momentum-space representation of the reduced Schrödinger-Coulomb Green’s function is obtained in closed form for all states n. Explicit forms are given for n=1 and 2.

A general treatment of the quantized harmonic oscillator with time-dependent mass and frequency is presented. The treatment is also applied to the time-dependent oscillator under the action of a time-dependent perturbative potential. The treatment is based on the use of some time-dependent transformations and in the method of invariants of Lewis and Riesenfeld [J. Math. Phys. 10, 1458 (1969)]. Exact coherent states for such systems are also constructed.

The variational method, within the Hamiltonian formalism of QED, is used to derive relativistic integral equations for two- and three-fermion systems, in the Fermi version of the Lorentz gauge. The results are shown to be the same as those obtained previously in the Coulomb gauge, provided the trial states are chosen to incorporate the same physical effects in each gauge.

I develop an alternative approach to the Rayleigh-Schrödinger perturbation theory that is based on a canonical transformation of the unperturbed operator into a first-order differential operator. As a result the perturbation formulas reduce to a hierarchy of first-order inhomogeneous differential equations that one can easily solve by quadratures for all the states simultaneously. I apply the method to the anharmonic oscillator, a perturbed Kratzer potential, and the LoSurdo-Stark effect in a two-dimensional hydrogen atom.

The induced non-Abelian gauge structure of the effective Hamiltonian arising from the Born-Oppenheimer approximation is investigated. It is shown that the trace of the electric part of the gauge potential is related to the natural metric on the complex Grassmannian of Hilbert subspaces. Our results are illustrated by a simple example yielding SU(2) gauge fields (instantons), and the corresponding electric gauge potential. The latter gives a contribution to the induced effective scalar potential. Electric gauge potentials associated with higher-dimensional monopoles are also obtained. For systems exhibiting such gauge structure it is shown that the sign of the effective scalar potential depends on the Abelian or non-Abelian character of the gauge group.

A stochastic model of a continuous nondemolition observation of a quantum system is presented. The nonlinear stochastic wave equation describing the posterior dynamics of the observed quantum system is solved for a free particle of mass m>0. It is shown that the dispersion of the Gaussian wave packet does not increase to infinity as for a free unobserved particle, but tends to the finite limit ${\mathrm{\tau }}_{\mathrm{\infty }}^2$=(ħ/2λm${)}^{1/2}$, where λ is the accuracy coefficient of an indirect nondemolition measurement of the particle’s position.

We solve the Dirac-particle problem exactly in two spatial dimensions by using the standard method of quantum mechanics and find that the inclusion of the δ function caused by intrinsic flux does not affect the final result. No irregular solution appears for any value of α and s.

The measuring process of an object system and a detector are studied in the von Neumann model and one of its variants, in which the detector consists of a single particle. If the states of the particle after the interaction with the object system are described partly by coherent states, then the particle can play the role of a detector under certain conditions. The mass (or free Hamiltonian) of the detector does not affect the measuring process at all, while the mass of the object system plays an important role. In the von Neumann model, if the mass of the object system is quite large, the position measurement can be considered, and under certain conditions the statistical operator ρ tends to just its mixed-state part, i.e., quantum interference disappears. However, when the time after the interaction becomes very large, interference emerges again. On the other hand, if the mass of the object system is small, we can even consider the momentum measurement and show that ρ approaches its mixed-state part when the time becomes very large, i.e., ρ is equivalent to its mixed-state part. The momentum can also be measured almost completely in the variant model; the operator ρ becomes equivalent to its mixed-state part. The different quantum states distinguish the detectors from the object systems.

We consider the geometrical phases arising in the state vector of two-level atoms due to their interaction with a self-consistently generated classical electrical field propagating without loss through the atomic medium. Three conservation laws are shown to exist generally and are used to solve for the individual quantum amplitudes, phases, and the electric field. We calculate the geometrical phases in two situations: (a) where the atoms are initially in the ground state and (b) where the initial state is a coherent superposition of the ground and excited states. In both cases the geometrical phase is the Aharonov-Anandan phase resulting from the atomic state vector tracing out a closed curve on the projective Hilbert space–here the Bloch sphere. We show that geometric quantities associated with the curve on the Bloch sphere are directly related to physical observables. The solid angle subtended by the closed curve (shown to equal twice the geometric phase) is a measure of the maximum atomic inversion, while the speed with which the curve is traced is related to the energy uncertainty in the state. An experimental method to observe the total phase change in a two-level subsystem is outlined, using photon echoes in a three-level medium.

The techniques of relativistic many-body calculations on atoms and ions have been used to reformulate the multiconfigurational Dirac-Fock techniques in such a way that good wave functions can be obtained with the same accuracy as with many-body perturbation theory, and a relationship between both approaches has been established. As an example the hyperfine interactions of the 7s, 7${\mathit{p}}_{1/2}$, and 7${\mathit{p}}_{3/2}$ states of ${\mathrm{Ra}}^{+}$ have been successfully calculated and are in good agreement with experiment.

We report magnetic-dipole hyperfine-structure constants for Scii 3${\mathit{d}}^{23}$${\mathit{P}}_{\mathrm{}(1,2)\mathrm{}}$ and Y ii 4${\mathit{d}}^{23}$${\mathit{P}}_{\mathrm{}(1,2)\mathrm{}}$ ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_{\mathrm{}\left(2\right)\mathrm{}}$, which unlike the Dirac-Fock results are in excellent agreement with experiment. Theoretical values are (-108.87, -30.49, 47.01, 11.25, -22.98 MHz), compared with experiment (-107.3, -27.9, 46.56, 11.60, -26.40 MHz). We also predict that the hyperfine constant for Y ii4${\mathit{d}}^{23}$${\mathit{F}}_2$ is -149.94 MHz. Our calculations were done with nonrelativistic (Sc ii) and relativistic (Y ii) many-body theory. We found it unnecessary to include any off-diagonal hyperfine-coupling effects.

Excitation energies and oscillator strengths from the ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ ground state to the first ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ and ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ excited states of Hg-like ions are calculated by using the multiconfiguration relativistic random-phase approximation. Results are compared with other theories and with experiment. The discrepancy between the theoretical and experimental results is discussed.

The production of the n=2 state of positronium by slow-positron bombardment is observed from well-characterized metal surfaces of Cu and W under UHV conditions. The maximum fractions observed are (2.73±0.13)×${10}^{\mathrm{-}3}$ for Cu and (3.70±0.53)×${10}^{\mathrm{-}3}$ for W. Measurements made as a function of incident-positron energy show a substantial difference in the incident-energy dependence for the Ps(n=1) and Ps(n=2) fractions, with W exhibiting a threshold for Ps(n=2) formation at an energy near 5 eV. These observations are consistent with Ps(n=2) formation as a result of charge capture at the surface by backscattered nonthermalized positrons. An understanding of the Ps(n=2) emission mechanism is important for improving the yields of excited-state production for fine-structure measurements.

Using a kinetic-energy-density functional with a modified ‘‘first-gradient’’ correction, Dirac exchange functional, and a parametrized Wigner-type local correlation functional, a simple quadratic equation is solved for the ground-state electronic densities and properties of atoms and ions, including alkaline-earth-metal singly charged negative ions. The results for various expectation values and the electrostatic potential compare quite favorably with near-Hartree-Fock and relativistic density-functional results, respectively.

A recently developed high-resolution dipole (e,e) method [W. F. Chan, G. Cooper, and C. E. Brion, Phys. Rev. A 44, 186 (1991)] for the measurement of absolute optical oscillator strengths (cross sections) for electronic excitation of free atoms and molecules has now been applied to photoabsorption and photoionization processes for neon in the energy range 16–250 eV. The absolute scale is obtained by Thomas-Reiche-Kuhn (TRK) sum-rule normalization of the Bethe-Born converted electron-energy-loss spectrum. The measured absolute photoabsorption oscillator strengths for discrete electronic transitions of neon from the ground state to the 2${\mathit{s}}^2$2${\mathit{p}}^5$ns and 2${\mathit{s}}^2$2${\mathit{p}}^5$nd${(}^2$${\mathit{P}}_{3/2,1/2}$) manifolds are compared where previously reported experimental data are available. Measurements of the absolute optical strength in the photoionization continuum up to 250 eV are compared with other experimental and theoretical data. Absolute optical oscillator strengths in the 40–55-eV region of the 2s2${\mathit{p}}^6$np and 2${\mathit{s}}^2$2${\mathit{p}}^4$3lnl’ autoionizing resonances are also reported.

In the approach proposed by Harbola and Sahni for the determination of electronic structure, the correlations between the interacting electrons are directly related to the local effective many-body potential in which they move by Coulomb’s law. As such this potential is the work required to move an electron in the force field of its Fermi-Coulomb-hole-charge distribution. In this paper we have applied this approach within the Pauli-correlated approximation, in which only correlations between the electrons due to the Pauli exclusion principle are considered, to atoms from He (Z=2) to Rn (Z=86). For open-shell atoms the central-field model is assumed. The calculations are also spin restricted and nonrelativistic. The self-consistently-determined atomic properties presented are the total ground-state energy, the highest-occupied-orbital eigenvalue, and the expectation value of the single-particle operators r,${\mathit{r}}^2$, ${\mathit{r}}^{\mathrm{-}1}$,${\mathit{r}}^{\mathrm{-}2}$, and δ(r). The total ground-state energies and expectation values are essentially equivalent to those of Hartree-Fock theory, with the relative differences diminishing with increasing atomic number. The total ground-state energies lie above, as must be the case, and within parts per million of the Hartree-Fock theory results. By ${}_{}{}^9{}_{}{}^{}\mathrm{F}$ this difference is 50 ppm, by ${}_{}{}^{35}{}_{}{}^{}\mathrm{Br}$ 10 ppm, and by ${}_{}{}^{72}{}_{}{}^{}\mathrm{Hf}$ less than 5 ppm.

The most remarkable results, however, are those for the highest-occupied-orbital eigenvalues. In the Harbola-Sahni approach, the asymptotic structure of the effective potential in the Pauli-correlated approximation is that of the fully correlated system, in which correlations between the electrons due to Coulomb repulsion are also considered. This is manifested by the fact that in comparison with Hartree-Fock theory, the highest-occupied-orbital eigenenergies for the majority of atoms are closer to the experimental ionization potentials. For the remaining atoms, the differences between the two theories are of the order of hundredths of a rydberg or less. Furthermore, we note that in the central-field model the density-functional-theory exchange-energy-potential sum rule due to Levy and Perdew is rigorously satisfied by the potentials and orbitals of this approach. For the present calculations this sum rule is satisfied numerically from six to eight significant figures, as is the virial theorem. Finally, the Harbola-Sahni approach in the Pauli-correlated approximation is contrasted to Hartree-Fock theory, and directions for future research to go beyond it within this framework are indicated.

In variational calculations of quantum mechanics, constraints are sometimes imposed explicitly on the wave function. These constraints, which are deduced by physical arguments, are often not uniquely defined. In this work, we will point out the advantage of parametrizing constraints and letting the variational principle determine the best possible constraint for the problem. Examples are carried out to show the surprising effectiveness of the variational method if constraints are parametrized. It is also shown that misleading results may be obtained if a constraint is not parametrized.

The expressions for two-center overlap integrals between angular s, p, and d Slater orbitals of arbitrary, higher principal quantum number are explicitly listed. The expressions obtained are extremely compact and independent of the coordinate system. It is further shown that the numerical values of the integrals obtained in this way are free from any numerical instability.

Calculations of the level width Γ(${\mathit{L}}_1$) and the ${\mathit{f}}_{12}$ and ${\mathit{f}}_{13}$ Coster-Kronig yields for atomic zinc have been performed with Dirac-Fock wave functions. For Γ(${\mathit{L}}_1$), a large deviation between theory and evaluated data exists. We include the incomplete orthogonality of the electron orbitals as well as the interchannel interaction of the decaying states. Orbital relaxation reduces the total rates in all groups of the electron-emission spectrum by about 10–20 %. Different, however, is the effect of the continuum interaction. The ${\mathit{L}}_{1\mathrm{-}}$${\mathit{L}}_{23}$X Coster-Kronig part of the spectrum is definitely reduced in its intensity, whereas the MM and MN spectra are slightly enhanced. This results in a reduction of Coster-Kronig yields, where for medium and heavy elements considerable discrepancies have been found in comparison to relativistic theory. Briefly, we discuss the consequences of our calculations for heavier elements.

The recent discovery by Richter and Wintgen [J. Phys. B 23, L197 (1990)] that the classical helium atom is not globally ergodic has stimulated renewed interest in its semiclassical quantization. The Einstein-Brillouin-Keller quantization of Kolmogorov-Arnold-Moser tori around stable periodic orbits becomes locally possible in a selected region of phase space. Using a hyperspherical representation we have found a dynamically confining potential allowing for a stable motion near the Wannier ridge. The resulting semiclassical eigenenergies provide a test for full quantum calculations in the limit of very high quantum numbers. The relations to frequently used group-theoretical classifications for doubly excited states and to the periodic-orbit quantization of the chaotic portion of the phase space are discussed. The extrapolation of the semiclassical quantization to low-lying states give remarkably accurate estimates for the energies of all symmetric L=0 states of helium.