Recently, systematic optimal control theory has been successfully applied to design optical fields which act on a molecule to guide or transform it into a specifically prescribed state. Under realistic laboratory conditions and for real molecules, it is inevitable that there will exist disturbances and uncertainties in the control optical field, in the molecular Hamiltonian, and in the field-coupling coefficient (e.g., the dipole moment), etc. Therefore, it is important to design an optimal field which is robust to disturbances. In this paper, we provide a method through which the worst possible disturbance to the control process, under certain possible constraints, can be calculated and a corresponding optimal control field designed to be robust to the disturbances. Under disturbances of small amplitude, a perturbation solution to this problem can be applied. Illustrations are given for control of the wave-packet evolution of a diatomic molecule in the presence of disturbances.

We present an overview of the contributions to the isotope shift of the 1S-2S transition between hydrogen and deuterium. We have calculated an additional contribution to the energy, due to the exchange of a virtual transverse photon between the electron and the deuteron. We also correct the previously evaluated finite-size and recoil contributions [F. Schmidt-Kaler et al., Phys. Rev. Lett. 70, 2261 (1993)]. Our result is 670 994 445(33) kHz, which is in disagreement with the experimental value of 670 994 337(22) KHz. This discrepancy is probably caused by an incorrect value for the deuteron radius.

The problem of connecting systems with different numbers of degrees of freedom is discussed. Constraints appropriate for ‘‘Bose’’ and ‘‘Fermi’’ quantization are used to construct algebras of Dirac brackets associated with special solutions of the nonlinear complex oscillator. The constraints are shown to provide a basis for characterizing the elementary excitations of the oscillators. An alternative notion of quantization through a correspondence with an enveloping subalgebra of the Dirac brackets is introduced, a notion which simplifies the operator-ordering problem implied by the original Dirac brackets. The infinite- and the two-dimensional representations of the subalgebra are utilized to illustrate the quantization technique.

We apply the quasilinearization method of Bellman and Kalaba [Quasilinearization and Nonlinear Boundary-Value Problems (Elsevier, New York, 1965)] to find approximate solutions for the multidimensional quantum tunneling for separable as well as nonseparable wave equations. By introducing the idea of the complex ‘‘semiclassical trajectory’’ which is valid for the motion over and under the barrier, and which, in the proper limit, reduces to the real classical trajectory in the allowed region, we obtain an eigenvalue equation for the characteristic wave numbers. This eigenvalue equation is similar to the corresponding equation obtained from the WKB approximation and yields complex eigenvalues with negative imaginary parts. When the barrier changes very rapidly as a function of the radial distance, we can replace the concept of the semiclassical trajectory, which may not be applicable in this case, by the concept of a complex ‘‘quantum trajectory.’’ The trajectory defined either way depends on a constant of integration, and by minimizing the action with respect to this constant we can obtain the minimum escape path. The case of two-dimensional tunneling is discussed as an example of this method.

On the basis of the q-binomial theorem we construct the q-binomial state for a q-deformed boson which interpolates between the q-number state and the q-coherent state. The properties of the q-binomial state are also discussed.

The effects on field observables due to the interaction with a moving dielectric slab is studied in Born approximation. The system is modeled by a one-dimensional scalar field coupled to a one-dimensional body with finite thickness. The formation of a cloud of virtual quanta after the switching on of the interaction and the effects of the acceleration of the body are discussed separately. It has been shown that there is emission of energy density waves after the body has a perturbation of its elsewhere constant motion, but not emission of overall energy.

The modal interpretation explained here construes the mathematical formalism of quantum mechanics in terms of physical properties (‘‘be-ables,’’ ‘‘existents’’) in such a way that the property attribution reflects the mathematical structure as much as possible—no additional structure is superimposed on the formalism. We generalize the interpretation by specifying a dynamics of physical properties, and also extend it while replying to recent objections by Albert and Loewer 2 [Proceedings of the 1990 Biennial Meeting of the Philosophy of Science Association, edited by A. Fine, M. Forbes, and L. Wessels (Philosophy of Science Association, East Lansing, MI, 1990), Vol. 1, p. 277], and by Elby [Found. Phys. Lett. 6, 5 (1993)]. I also discuss questions relating to relativistic aspects and casuality.

We use separation of variables as a tool to identify and to analyze exactly soluble time-dependent quantum-mechanical potentials. By considering the most general possible time-dependent redefinition of the spatial coordinate, as well as general transformations on the wave functions, we show that separation of variables applies and exact solubility occurs only in a very restricted class of time-dependent models. We consider the formal structure underlying our findings, and the relationship between our results and other work on time-dependent potentials. As an application of our methods, we apply our results to the calculation of propagators.

An information-theory-based approach to the semiclassical treatment of the N-fermion problem is presented which improves upon the traditional ones in two respects: It is valid beyond the turning points and is able to describe shell effects. The method is illustrated by recourse to simple one-dimensional systems.

The quantum characteristics of chaotic systems are usually studied using microwave cavities. For these cavities we use a model in terms of lumped circuits based on the equivalence between the transfer functions characterizing a cavity, and a set of coupled RLC resonators. Avoided crossings, cluster distribution of the energy levels, and eigenfunction localization effects are analyzed. The ordering and spacing of eigenfrequencies in a cluster, and the oscillation amplitudes of the resonators are presented for symmetric cavities. The predictions of the model are in close concordance with the existing numerical and experimental data.

A position-measurement scheme is discussed which prepares an atom in a contractive state. Two operating regimes are analyzed. In the first, the quadratic form of the interaction potential is responsible for the focusing. In the second regime the potential varies approximately linearly with position, and the focusing results from the measurement itself. In this second regime the scheme provides a very close realization of the Einstein-Podolsky-Rosen Gedankenexperiment, an analogy that allows some insight into the production of measurement-induced contractive states.

A semiclassical propagator is applied to describe the dynamics of circular-orbit wave packets which are initially well localized in three dimensions. A sum over classical Kepler trajectories for the wave-packet autocorrelation function is obtained which is extremely accurate well past the classical regime of the evolution regime of the wave packet. The nonclassical nature of the wave-packet evolution at long times is associated with the interference between amplitudes from classical paths at different energies. The time scale of the wave-packet revivals is related to the shearing rate of the corresponding classical ensemble.

Three-dimensional, spherically symmetric Hamilton operators, which consist of the sum of an arbitrary effective kinetic energy and an attractive Coulomb potential, are quantized semiclassically. The semiclassical quantization rule that we derive passes the test of estimating the Bohr energies of hydrogenlike atoms successfully. The semiclassical spectrum of Thomas-Fermi atoms, which are described in terms of an effective kinetic energy, is found to agree essentially with the spectrum obtained in the standard formalism that employs an effective potential energy.

We report a measurement of the lifetime of the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ state in two-electron krypton. The lifetime is found to be 171.0±2.2 ps, which is in reasonable agreement with current theoretical calculations. This measurement provides a test of the order (Zα${)}^2$ relativistic corrections to this lifetime.

Based on the recent paper of Yasuhara and Takada [Phys. Rev. B 43, 7200 (1991)] on a screened-exchange potential for band calculations, an improvement is made on the correlated Hartree-Fock method for inhomogeneous many-electron systems so as to yield excellent results for both the total energies and the ionization potentials of atoms in the Periodic Table from He to Ca.

We report the results of an accurate measurement of the optical oscillator strengths of the prominent resonance lines of He, Ne, Ar, and Kr in the vacuum-ultraviolet region based on the absorption of resonance radiation. The transmission of this radiation through a layer of gas of finite thickness is measured as a function of the number density of the gas. The transmission function is fitted to this data to obtain the absorption oscillator strength. The accuracy of the present measurements ranges from 2.5% to 4%. The results are as follows: He i (58.4 nm), 0.2683±0.0075 (2.8%); He i (5.37 nm), 0.0717±0.0024 (3.4%); Ne i (74.4 nm), 0.010 17±0.000 30 (2.9%); Ne i (73.6 nm), 0.1369±0.0035 (2.6%); Ar i (106.7 nm), 0.0616±0.0021 (3.4%); Ar i (104.8 nm), 0.2297±0.0093 (4.0%); Kr i (123.6 nm), 0.1751±0.0049 (2.8%); Kr i (116.5 nm), 0.1496±0.0038 (2.5%).

The hyperfine splitting of a soft-x-ray lasing line coming from neonlike niobium has recently been measured and the effect of the splitting on the gain coefficient observed, as reported earlier. In this work, the hyperfine splittings for the principal 3p→3s neonlike lasing lines due to the coupling with the dipole magnetic moment of the nucleus are calculated for atomic numbers Z from 17 through 59 in the framework of the relativistic multiconfiguration-atomic-structure theory. The diminution of the gains due to splittings in the case of Doppler-broadened lines is calculated. The parameters for the splitting of the 2p-to-2s transitions in fluorinelike ions and the 3p-to-3s and 3d-to-3p transitions in sodiumlike ions are also presented.

Ion production by low-energy positrons in low-density gases was reported by Passner, Surko, Mills, and Leventhal [Phys. Rev. A 39, 3706 (1989)]. That work studied the ionization of hydrocarbons in a positron trap in the presence of a buffer gas of molecular nitrogen. We present further analysis of the data from this experiment, taking into consideration the ionization of the hydrocarbons by nitrogen ions created as a result of the positron trapping process. We conclude that ionization by positrons was the dominant ion production mechanism at times longer than the characteristic ion confinement time of approximately 1 s, while ionization by nitrogen charge exchange was dominant at earlier times. The details of the ionization spectra are also discussed.

Excitation energies and oscillator strengths from the ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ ground state to the first ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1^{\mathit{o}}$ and ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1^{\mathit{o}}$ excited states of Zn-like ions are calculated by using the multiconfiguration relativistic random-phase approximation including excitation channels from core electrons. The disagreements among theories and experiments are much reduced but in general remain.

We have determined theoretical values for the excitation energy, optical oscillator strength, and generalized oscillator strength (GOS), as well as experimental values for the GOS for the C 1s (1${\mathrm{\sigma }}_{\mathit{g}}$→1${\mathrm{\pi }}_{\mathit{g}}$) and (1${\mathrm{\sigma }}_{\mathit{u}}$→1${\mathrm{\pi }}_{\mathit{g}}$) transitions in the ${\mathrm{C}}_2$${\mathrm{H}}_2$ molecule. In order to study the influence of relaxation, correlation, and hole-localization effects on these properties, several calculations with different target wave functions were computed. The experimental results for the GOS were determined using a crossed-beam electron energy-loss spectrometer.