Constructions of local potentials with positive eigenvalues for the one-particle Schrödinger equation are presented. The complete transparency of these potentials, manifesting itself in vanishing scattering phases for potentials over the semiaxis and vanishing reflection coefficients with transmission coefficients equal to one for the full axis, is shown. The results derived here via Darboux transformations are compared with those obtained in similar approaches such as the double commutation method, the Gel’fand-Levitan formalism, or supersymmetric quantum mechanics. An application within the theory of nonlinear waves is indicated.

A mathematical representation of measurements on geometric excitations is given for the geometric unified theory. Application to excitations generated by rotations results in quantum numbers nħ/2 for a geometric angular-momentum current. Excitations generated by the other compact subgroup result in quantum numbers qe for the geometric electric charge. The method is compatible with quantum mechanics but additionally gives the quantum of electric charge.

An approach to study the time-dependent quantum oscillator with the Schrödinger operator S(Ω(t))≡1/2[${\mathbf{p}}^2$+${\mathrm{\Omega }}^2$(t)${\mathbf{x}}^2$]-i(∂/∂t) is presented. A family of unitary operators {${\mathbf{W}}_{1\mathit{z}}$(t)} is found such that S(Ω(t))=${\mathbf{W}}_{1\mathit{z}}$(t)S(ω)${\mathbf{W}}_{1\mathit{z}}^{\mathrm{°}}$(t), where z=z(t) is a certain function and ω is a positive number. Wave vectors, the boson creation and destruction operators, the evolution operator, and invariants for the time-dependent oscillator are obtained by means of {${\mathbf{W}}_{1\mathit{z}}$(t)}. The approach is applied to calculate transition probabilities, Berry phases, and to study coherent states of the time-dependent oscillator.

In this paper we analyze the controllability of quantum systems arising in molecular dynamics. We model these systems as systems with finite numbers of levels, and examine their controllability. To do this we pass to their unitary generators and use results on the controllability of invariant systems on Lie groups. Examples of molecular systems, modeled as finite-dimensional control systems, are provided. A simple algorithm to detect the controllability of a molecular system is provided. Finally, we apply this algorithm to a five-level system.

The influence of continuous measurements of energy with finite accuracy is studied in various quantum systems through a restriction of the Feynman path integrals around the measurement result. The method, which is equivalent to considering an effective Schrödinger equation with a non-Hermitian Hamiltonian, allows one to study the dynamics of the wave-function collapse. A numerical algorithm for solving the effective Schrödinger equation is developed and checked in the case of a harmonic oscillator. The situations, of physical interest, of a two-level system and of a metastable quantum well are then discussed. In the first case, the Zeno inhibition observed in quantum optics experiments is recovered and extended to nonresonant transitions, and in the second case we propose an observation of the inhibition of spontaneous decay in mesoscopic heterostructures. In all the considered examples, the effect of the continuous measurement of energy is a freezing of the evolution of the system proportional to the accuracy of the measurement itself.

We investigate the outcome of measurements on correlated, few-body quantum systems described by a quaternionic quantum mechanics that allows for regions of quaternionic curvature. We find that a multiparticle interferometry experiment using a correlated system of four nonrelativistic, spin-half particles has the potential to detect the presence of quaternionic curvature. Two-body systems, however, are shown to give predictions identical to those of standard quantum mechanics when relative angles are used in the construction of the operators corresponding to measurements.

The quantum-mechanical version of the four kinds of classical canonical transformations is investigated by using non-Hermitian operator techniques. To help understand the usefulness of this approach, the eigenvalue problem of a harmonic oscillator is solved in two different types of canonical transformations. The quantum form of the classical Hamilton-Jacobi theory is also employed to solve time-dependent Schrödinger wave equations, showing that when one uses the classical action as a generating function of the quantum canonical transformation of time evolutions of state vectors, the corresponding propagator can easily be obtained.

Given an entanglement of two systems involving nonorthogonal states, we find the Schmidt decomposition for the state. The relation between the Schmidt representation and an ideal measurement of the degree of entanglement of the states is discussed, and a Bell inequality is shown to be violated. The maximal violation of the Bell inequality provides a measurement of the degree of entanglement. The entangled coherent states are provided as a concrete example of the Bell inequality for entangled nonorthogonal states.

The effects of the inevitable coupling to external degrees of freedom of a quantum computer are examined. It is found that for quantum calculations (in which the maintenance of coherence over a large number of states is important), not only must the coupling be small, but the time taken in the quantum calculation must be less than the thermal time scale ħ/${\mathit{k}}_{\mathit{B}}$T. For longer times the condition on the strength of the coupling to the external world becomes much more stringent.

We study higher-order effects in the electromagnetic production of electron-positron pairs in relativistic heavy-ion collisions. Treating the field of the heavy ions as an external field and neglecting the interaction among electrons and positrons, we show that the N-pair creation amplitude is the antisymmetrized product of N one-pair creation amplitudes and the vacuum amplitude. Neglecting contributions coming from exchange terms, we show that the total probability for N pairs is approximately a Poisson distribution. We investigate further the structure of the reduced one-pair amplitude, concentrating especially on multiple-particle corrections. We calculate the first of these corrections in second-order Magnus theory based on our previous result [Phys. Rev. A 49, 1584 (1994)] in the second-order Born approximation for impact parameter b zero. Explicit calculations show that the total probability is increased up to 10% by this correction for realistic collider parameters. The calculations can also be used to confirm the use of the Poisson distribution for the total probability.

We have obtained spectra of the high-lying vibrational levels of the $1^3$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$ state of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_2^{}{}_{}{}^{}$ via photoassociation of ultracold ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ atoms confined in a magneto-optical trap. The $1^3$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$ state of the diatomic molecule correlates to a 2${\mathit{S}}_{1/2}$ state atom plus a 2${\mathit{P}}_{1/2}$ state atom. The long-range part of the molecular interaction potential for this state depends on the 2P atomic radiative lifetime. By calculating the energy eigenvalues of a model potential for the $1^3$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$ state and fitting them to the experimentally measured vibrational levels, we have extracted a value for the 2P lifetime of 26.99±0.16 ns. The precision is currently limited by the accuracy of a region of the model potential provided by ab initio calculations.

We calculate the contribution of the six radiatively corrected light-by-light scattering graphs to the decay rate of orthopositronium. Our result is ${\mathrm{\Gamma }}_{\mathrm{light}\mathrm{-}\mathrm{by}\mathrm{-}\mathrm{light}}$= -${\mathrm{\alpha }}^2$ln(1/α)${\mathrm{\Gamma }}_{\mathrm{LO}}$+9.0074(9)(${\mathrm{\alpha }}^2$/${\mathrm{\pi }}^2$)${\mathrm{\Gamma }}_{\mathrm{LO}}$. Our result contains a known analytic logarithm plus a new constant term which contributes 0.000 350 μ${\mathrm{s}}^{\mathrm{-}1}$ to the rate.

The total decay probabilities per unit time of the first excited 9.4-keV state in ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$ have been measured in ions of ionicity q from 28 to 32. Using a γ-decay probability per unit time of 0.255(2)×${10}^6$ ${\mathrm{s}}^{\mathrm{-}1}$ gives internal conversion coefficients of 14.6(11), 14.9(10), 14.1(9), 14.6(11), and 15.2(24) for q=28–32, respectively. These values are compared with theoretical predictions.

Single-photon ionization of an atom or molecule can be subdivided into parity-favored and -unfavored transitions, the latter characterized by electron emission, preferentially perpendicular to the electric vector. The nonresonant existence of these transitions is shown experimentally and studied over an extended energy range for a variety of satellite transitions in atomic argon. The spectra exhibit several clearly resolved satellite lines with strongly negative β values close to -1, independent of the photon energy. The results confirm the corresponding predictions of angular-momentum transfer theory.

We examine the fragment spin multiplicities in the fission ${\mathrm{Ag}}_{23}^{2+}$→${\mathrm{Ag}}_{12}^{+}$+${\mathrm{Ag}}_{11}^{+}$ using the jellium model which allows axially symmetric deformations and fission. The fission is investigated along two fission paths, one leading to two prolatelike fragments and the other resulting in two oblatelike fragments. It is shown that the former path produces the low-spin ${\mathrm{Ag}}_{11}^{+}$(S=0) and the low-spin ${\mathrm{Ag}}_{12}^{+}$(S=1/2), but the latter path produces the high-spin ${\mathrm{Ag}}_{11}^{+}$(S=1) and the high-spin ${\mathrm{Ag}}_{12}^{+}$(S=3/2). Therefore the ratio of fission barriers along the two different paths will be estimated from the abundance ratio of two different spin fragments.

Accurate measurements are presented of the rate of trap-loss-producing collisions between ultracold magneto-optically trapped ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ atoms for a range of trap laser intensities and frequencies. Intensities from near the atomic saturation intensity to well above it are investigated. At low intensities, fine-structure-changing collisions cause trap loss with a rate constant of ∼${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$/s. At sufficiently high intensity, the trap can be deep enough to effectively freeze out the dominant fine-structure-changing collisions as a loss mechanism, enabling an accurate comparison of the radiative escape loss rate with theory. At the lowest intensities of this radiative escape regime, the measured loss rates compare favorably with those calculated using an optical Bloch equation theory and a three-dimensional model of trap depth. However, the intensity dependence of the measured rates does not show the saturation predicted by the optical Bloch equation theory. It is shown that reliable knowledge of trap depth is necessary to accurately compare experiment with theory.

Lifetimes of NO p- and f-orbital Rydberg states (n=40–122) have been measured under near field-free conditions as well as in the presence of small dc electric fields. The field causes an increase in the observed lifetimes, which is attributed to Stark mixing of the predissociative p and f orbitals with high-l orbital angular momentum states. The results indicate that under the conditions existing in high-resolution zero-electron-kinetic-energy (ZEKE) photoelectron spectroscopy experiments, the ZEKE Rydberg states are l mixed.

Multiphoton ionization of cesium atoms has been studied with both linearly and circularly polarized light pulses of 1.9-μm wavelength. Photoelectron energy spectra show that the use of circular polarization leads to a strong reduction of above-threshold ionization (ATI), in comparison to linear polarization, and not to suppression of low-order ATI peaks. This behavior is different from that expected for hydrogen under similar circumstances. Calculations reproduce the behavior of cesium and indicate that it can be attributed to the large size of the ground state of cesium.

Experimental measurements of the absolute energy yields and conversion efficiencies of high-order harmonic radiation in the spectral range of 31 to 17 nm are presented. We examine energy yields as a function of a number of parameters including drive laser wavelength, target atom, focal geometry, and peak laser intensity, and we have generated individual harmonics with energies as high as 60 nJ at wavelengths as short as 20 nm. Under optimum conditions, we find that conversion efficiencies of as high as ${10}^{\mathrm{-}7}$ into each harmonic are possible.

We have measured the far-field angular distributions of high harmonics (orders 11–41) generated by a 1-μm, 1-ps laser pulse [(0.3–3)×${10}^{14}$ W/${\mathrm{cm}}^2$] in low-density Ar, Kr, and Xe targets (≤1 Torr, 1-mm thick). The far-field harmonic distributions show a narrow central structure surrounded by broad wings that contain approximately 75% of the harmonic energy. Low-density targets and f/70 focusing were used to minimize phase mismatches due to ionization and propagation effects, thereby isolating the single-atom contribution to the response. The wings indicate an intensity-dependent phase of the atomic harmonic emission.