A particle moves in one spatial dimension in an attractive symmetric potential vf(x) and obeys nonrelativistic quantum mechanics. It is supposed that the trajectory function F(v), which tells us how the ground-state energy depends on the coupling parameter v, is known. We determine the minimum f(0) of the potential and the mean kinetic energy s(v) from F(v), and we prove that the potential shape f(x) has the constant value f(0) on an interval [-a,a] if and only if s is bounded for all v>0. Moreover, if s<K, then a>(π/2)[ħ/(2mK)${]}^{1/2}$. These are partial results towards geometric spectral inversion, the determination of the potential shape f from the corresponding ground-state energy trajectory F.

The statistics of quantum optical phase observables are recovered as patterns from both number as well as phase-space measurement statistics. A model for the measurement of generalized Q functions studied recently by Leonhardt and Paul [Phys. Rev. A. 47, R2460 (1993); 48, 3265 (1993)] is shown to yield measurements of arbitary phase-space observables.

We consider a two-slit diffraction experiment with a magnetic flux confined to an inaccessible region between two rectangular slits. We then obtain a leading-order analytic form for the asymmetry in the resulting diffraction pattern. The corrections to the expression are bounded and disappear in the limit of long wavelengths and/or infinite source-slit-screen spacing. Using the analytic form obtained, we obtain a nonzero value for the asymmetry in the number of electrons scattered to the left and to the right but a zero value for their average displacement.

We cast the quantum mechanics of multichannel systems in the broader mathematical framework of Hamiltonian phase space flow. This flow results from symplectic transformations that preserve antisymmetric products, namely, metric relations among alternative solutions with the same dynamics. This viewpoint affords new insight into recent successful phase-amplitude methods.

A nonrelativistic theory of the radiation reaction interaction is formulated, which is based on the strict implementation of the uncertainty prinicple into classical theory. The same idea is used in formulating the semiclassical theory of the radiation reaction interaction. The semiclassical and classical formulations give the same answer for the dynamics of a particle in a plane electromagnetic wave.

We propose two experiments involving Rydberg atoms and a high-Q microwave cavity. By preselecting and postselecting carefully the state of a single atom that crosses the cavity we obtain dramatic effects on the state of the rest of the system.

The Green’s functions of the recently discovered conditionally exactly solvable potentials are computed. This is done through the use of a second-order differential realization of the so(2,1) Lie algebra. So we present the dynamical symmetry underlying the solvability of such potentials and show that they belong to a general class of solvable and partially solvable potentials.

We derive unitary-operator images corresponding to classical phase-space symplectic transformations in the n-mode canonical coherent-state representation. The evaluation can be greatly facilitated by the technique of integration within an ordered product of operators, showing clearly the connection between symplectic transformations and the corresponding normally ordered unitary operators. Applications of these operators results in the construction of generalized coherent states.

The ground-state energies of hydrogenic atoms in a uniform magnetic field of arbitrary strength have been calculated accurately. A claim relating the energy eigenvalues of the nonseparable Hamiltonian H=-${\mathrm{\nabla }}^2$/2-Z/r+${\lambda }^2$(${\mathrm{x}}^2$+${\mathrm{y}}^2$)/2 to those of the spherically symmetric Hamiltonian H′=-${\mathrm{\nabla }}^2$/2-Z/r+${\lambda }^2$${\mathrm{r}}^2$/2 has been introduced and justified at the weak- and strong-magnetic-field limits. Moreover, the shifted 1/N expansion technique has been used to calculate the energy eigenvalues of H′.

The branching between predissociation and photoemission is measured using a fast beam technique for several excited singlet states of the nitrogen molecule that lie at energies between 110 000 and 113 000 ${\mathrm{cm}}^{\mathrm{-}1}$ above the ground electronic state. The specific states probed in this study are b’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$(v=9–13), c’ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$(v=3,4), and ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{+}{}_{}{}^{}$(v=3,4), and substantial predissociation is observed in each. The present measurements are compared with previous measurements of the branching ratio and with the predissociation rates implied by previous lifetimes and absorption linewidth measurements.

The recently introduced nonvariational spline-Galerkin method [T. Brage and C. Froese Fischer, Phys. Scr. 49, 651 (1994)] for Rydberg series is applied to the J=0, 1, 2, and 3 even states between the two first limits in neutral calcium. Energies for 3dnl levels up to n=15–20 are reported and the position of different perturbers belonging to the 4${\mathit{p}}^2$ and 4p5p configurations are investigated. The 4p5p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ level is predicted to have an excitation energy of about 61 200 ${\mathrm{cm}}^{\mathrm{-}1}$ and the 4p5p ${}_{}{}^3{}_{}{}^{}$D level is predicted at about 61 600–62 000 ${\mathrm{cm}}^{\mathrm{-}1}$, while the 4p5p ${}_{}{}^3{}_{}{}^{}$P is just at the 3d ${}_{}{}^2{}_{}{}^{}$D limit.

The accurate calculation of the static hyperpolarizability of the lithium atom poses a challenge to contemporary electronic structure methods. An extensive investigation of the effects of electron correlation and one-particle basis-set choice is carried out. The dipole polarizability and hyperpolarizability of Li are predicted to be 164.2±0.1${\mathit{e}}^2$${\mathit{a}}_0^2$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}1}$ and 2900±300${\mathit{e}}^4$${\mathit{a}}_0^4$${\mathit{E}}_{\mathit{H}}^{\mathrm{-}3}$, respectively, where ${\mathit{E}}_{\mathit{H}}$ is a hartree. Our best finite-field computation uses a (20s11p9d5f)/[13s10p9d5f] basis set of contracted Gaussians, and the CCSD(T) method, that is, the coupled cluster method in the space of single and double substitutions corrected noniteratively for triple substitutions.

We develop an efficient method for the calculation of corrections to the Born-Oppenheimer approximation by means of perturbation theory. The perturbation terms through sixth order in the small parameter κ=(m/M${)}^{1/4}$, where m and M are, respectively, electronic and nuclear masses, allow the construction of an effective vibrational Hamiltonian that takes into account adiabatic and nonadiabatic effects. The latter is negative and linearly dependent on the vibrational quantum numbers. We illustrate the application of the main equations and verify the general results by means of an exactly solvable model of two coupled harmonic oscillators.

New results are reported in our search for the electric dipole moment ${\mathit{d}}_{\mathit{e}}$ of the electron in the ground 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$ state of ${}_{}{}^{205}{}_{}{}^{}\mathrm{Tl}$. The atomic-beam magnetic resonance method is employed with separated oscillating fields. A magnetic field B defines the axis of quantization, and an electric field E, parallel to B, is applied in the region between the oscillating fields. Laser optical pumping is used for state selection and analysis, and the signal is fluorescence accompanying the decay of excited atoms in the analyzer region. The signature of a nonzero electric dipole moment is a dependence of the signal on the P,T-odd rotational invariant E⋅B (P and T denote parity and time reversal, respectively). Two counterpropagating atomic beams are employed to reduce a systematic effect due to the motional magnetic field E×v/c. Auxiliary experiments are performed to isolate and eliminate residual sources of systematic error. The result is ${\mathit{d}}_{\mathit{e}}$=[1.8±1.2(statistical)±1.0(systematic)]×${10}^{\mathrm{-}27}$ e cm. A detailed discussion is given of the experimental method, sources of systematic error and their elimination, and results.

The ${\mathrm{N}}_2$ C ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{}{}_{}{}^{}$ lifetime was measured by laser-induced fluorescence (LIF) in a low-density plasma. To take account of radiation trapping efects, the lifetime was measured as a function of LIF signal amplitude, which is also a measure of the ${\mathrm{N}}_2$ B ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathit{g}}^{}{}_{}{}^{}$ density. To first order, radiation trapping is linearly proportional to B-state density. By extrapolating the data to zero density, values around 40.5±2 nsec were found for the C-state lifetime.

Configuration-interaction wave functions are constructed for the lowest 11 atomic target states of neutral fluorine. These wave functions are used to calculate target-state energies and absorption oscillator strengths for the dipole-allowed transitions. In general, a good agreement is found between the length and velocity forms of f values. However, f values for some transitions show significant discrepancies between these two forms. All these target states are retained in the R-matrix basis function and the (N+1)-electron collision wave functions are expanded in terms of these basis functions. The calculations are performed for the electron-impact excitation collision strengths for all transitions between these states using the R-matrix method. In the low-partial-wave region (total angular momentum L≤12) the full exchange R-matrix method is employed while a no-exchange R-matrix method is used for the calculations in the partial-wave region with 13≤L≤40. The effect of this procedure is most evident in the case of dipole-forbidden transitions for which collision strengths increase by about 10–60 % due to the contribution from higher partial waves. Beyond this value of the total angular momentum, the Burgess sum rule is applied to determine the higher partial-wave contribution to the total collision strengths for dipole-allowed transitions. The collision strengths are obtained for a wide range of incident electron energy from the first excitation threshold to 3.0 Ry. The calculations are performed in the LS-coupling scheme.

We develop an alternative calculation method for the nth-order nonlinear optical susceptibilities ${\mathrm{\chi }}_{\mathrm{g}}^{\mathrm{}\left(\mathrm{n}\right)\mathrm{}}$(ω), for N-state quantum systems interacting with intense polychromatic fields, by means of the Fourier transformation of numerically exact solutions of the Liouville equation. This is a nonperturbative method that can provide both real and imaginary nonlinear optical spectra, valid for arbitrary laser intensities, frequencies, and relaxation. As applications of the method, we examine two types of three-, four-, and sixteen-state models that mimic the electronic excited states of trans octatetraene obtained from a full configuration-interaction calculation using the Pariser-Parr-Pople Hamiltonian. We also analyze the characteristics of the spectra in the off-resonance region for these models based on virtual excitation processes derived from the perturbative approach, and show that the second ${\mathrm{A}}_{\mathrm{g}}^1$ excited state above the first ionic ${\mathrm{B}}_{\mathrm{u}}^1$ state is essential for describing a qualitative ${\mathrm{\chi }}_{\mathrm{g}}^{\mathrm{}\left(3\right)\mathrm{}}$(ω) value rather than the first ${\mathrm{A}}_{\mathrm{g}}^1$ excited state below the first ${\mathrm{B}}_{\mathrm{u}}^1$ state. Furthermore, the characteristics of variations in the real part of ${\mathrm{\chi }}_{\mathrm{g}}^{\mathrm{}\left(3\right)\mathrm{}}$(ω) with the transition properties (transition energies and moments) of each excited state are elucidated both for a model only including the off-resonance process and a model including a two-photon resonance process.

A comprehensive quantum-mechanical description of resonant and nonresonant radiative transitions in complex electronic systems is developed, using a density-matrix approach. Specific applications are made to the unified treatment of radiative and dielectronic recombination of electrons with many-electron ions in high-temperature plasmas and to the unified treatment of transverse bound-bound and free-bound radiative transitions of energetic electrons channeled in crystal lattices. Both time-independent (resolvent-operator) and time-dependent (equation-of-motion) formulations of the density-matrix approach are presented. Liouville-space projection-operator techniques, which have been developed in the nonequilibrium quantum-statistical-mechanics description of relaxation phenomena, are employed. Self-consistent treatments are achieved for the excited-level populations and the spectral-line shapes. Applications are discussed for the broadening of atomic spectral lines by autoionization processes, radiative transitions, charged-particle collisions, and the action of the plasma electric microfields, and also for electron-channeling-radiation broadening by electron-electron, electron-photon, and electron-phonon interactions in a crystal lattice. The unified treatment of resonant and nonresonant radiative transitions is accomplished by means of a partition of the “relevant” Liouville space into separate subspaces corresponding to discrete resonance and nonresonant continuum states of the electronic system of interest. Although only single-photon processes are considered and only lowest-order quantum-electrodynamical perturbation theory is explicitly evaluated for the electron interaction with the radiation field, the general resolvent-operator and propagator formulations that are presented in this investigation can be applied to the description of multiphoton processes and, with the adoption of a suitable renormalization program, to the incorporation of radiative corrections to the transition probabilities.

A very efficient technique for the finite-basis-set calculation of logarithmic sums is introduced. The basis sets contain sequences of nonlinear parameters determined by the zeros of Laguerre polynomials. It is shown that one can easily obtain convergence to 12 digits in fast calculations involving small basis sets. The method is then applied to calculations of the asymptotic expansion of the Bethe logarithm for the Rydberg states of helium. As perturbation calculations of the sums involved diverge, the present method is used to obtain accurate results for atoms in dipole and quadrupole fields from which the adiabatic contributions are extracted. A discussion of gauges in the multipole case and the suppression of roundoff errors by working in a mixed gauge is presented. A strategy for handling the nonadiabatic contributions to sums is presented and used to obtain preliminary bounds on these contributions.

A variational method, based on some results due to T. Kato [Proc. Phys. Soc. Jpn. 4, 334 (1949)], and previously discussed is here applied to the hydrogen atom in uniform magnetic fields of tesla in order to calculate, with a rigorous error estimate, energy eigenvalues, energy eigenfunctions, and oscillator strengths relative to Rydberg states up to just below the field-free ionization threshold. Making use of a basis (parabolic Sturmian basis) with a size varying from 990 up to 5050, we obtain, over the energy range of -190 to -24 ${\mathrm{cm}}^{\mathrm{-}1}$, all of the eigenvalues and a good part of the oscillator strengths with a remarkable accuracy. This, however, decreases with increasing excitation energy and, thus, above ∼-24 ${\mathrm{cm}}^{\mathrm{-}1}$, we obtain results of good accuracy only for eigenvalues ranging up to ∼-12 ${\mathrm{cm}}^{\mathrm{-}1}$.