A method to measure the deviation from the linear law of superposition of angular velocities is proposed. The main advantage of the method is replacement of the rotating body by a stationary electro-optical medium with a rotating optical indicatrix.

Quantum mechanics gives us information about the spectra of dynamical variables and transition rates including scattering cross sections. They can be exhibited as spectral information in analytically continued spaces and their duals. Quantum mechanics formulated in these generalized spaces is used to study scattering and time evolution. It is shown that the usual asymptotic condition is inadequate to deal with the scattering of composite or unstable particles. Scattering theory needs an amendment when the interacting system is not isospectral with the free Hamiltonian; the amendment is formulated. Perturbation theory in generalized spaces is developed and used to study the deletion and augmentation of the spectrum of the Hamiltonian. A complete set of algebraically independent constants for an interacting system is obtained. The question of the breaking of time symmetry is discussed.

We study a quantum-mechanical rotor driven by two traveling potential-energy waves. We show that the decay properties of momentum-space wave functions can be predicted using a quantum renormalization map. We describe the results of numerical simulations of the Schrödinger equation, and compare the map’s predictions to the behavior observed in the simulations.

We derive quasiclassical (approximately factorizable) trajectories for the spin-boson Hamiltonian without the rotating-wave approximation (RWA) and show how they may be used to calculate the evolution of the fully quantized system when the initial state of the oscillator (boson field) is a coherent state with sufficiently large amplitude. We give a general prescription to obtain such trajectories for other systems. We study how well-known features of the model in the RWA are modified by the counterrotating terms and explore some of the new phenomenology introduced by these terms.

The spectrum of a relativistic electron in a uniform magnetic field is completely analyzed using supersymmetry quantum mechanics. The Dirac Hamiltonian less the rest energy is the supersymmetric Hamiltonian. Not only the electron (or positron) states with opposite helicities, but also the electron and positron states with opposite helicities, are shown to be superpartners. The degeneracy between the electron and positron ground states, as well as excited states with the same helicities, is shown to be due to the spontaneous breaking of symmetry under the combined operation of charge conjugation and time reversal.

We have solved, by numerical methods, the time-dependent Schrödinger equation for the known potential of electrons over the surface of liquid helium. The computed tunneling rates for a static field agreed with experimental measurements of the rates. We describe here the extension of the computation to time-dependent electric fields. The results provide quantitative details of the amplitude and frequency dependence of the tunneling rates. They show very large photoassisted enhancements of the tunneling rates. In addition, we find a modulation of the tunneling rates at the frequency of the applied field. The modulation amplitude decreases sharply at frequencies that are integer fractions of the frequency corresponding to the energy difference between the electron ground state and the top of the barrier. We find no evidence of finite transit-time effects.

Both spontaneous and stimulated radiation emitted by an electron beam traversing a periodic medium are studied in the approximation of neglecting the influence of the field on the motion of the electrons. The results are valid both in the vicinity of the Bragg domain as well as far from it. In the latter case, we recover previous results with some corrections. In the Bragg domains the result is of interest since in this case the emission of quanta increases considerably.

The Landé subtraction method is a technique for removing the singularity which arises when one solves the Schrödinger equation in momentum space for the Coulomb potential. Using this technique, numerical solutions for eigenvalues and eigenfunctions are presented and compared to exact results. Approximately 50 eigenvalues can be calculated very accurately for various values of the angular momentum. Numerous eigenfunctions can also be found very accurately. In addition, it is shown how to implement the Landé subtraction method for potentials which are a linear combination of the Coulomb potential and some other potential. Using a basis-function expansion technique, it is shown how to obtain solutions in those cases where the momentum integrals must be evaluated explicitly.

The influence of space-time curvature on quantum matter which can be theoretically described by covariant wave equations has not been experimentally established yet. In this paper we analyze in detail the suitability of the Ramsey atom beam interferometer for the measurement of the phase shift caused by the Riemannian curvature of the Earth or alternatively of two parallel oriented lead blocks. It appears that for the lead blocks the detection should be possible with realistic modifications of existing devices within the near future. For the Earth’s gravitational field the experimental difficulties are too big. The paper is divided into two parts. The first one is concerned with the derivation of general relativistic correction terms to the Pauli equation starting from the fully covariant Dirac equation and their physical interpretation. The inertial effects of acceleration and rotation are included. The calculation makes use of Fermi coordinates. In the second part we calculate the shift of the Ramsey fringes for the two different sources of curvature and examine various possibilities to enlarge the sensitivity of the apparatus to space-time curvature. Since the two parts may be more or less interesting for physicists with different research fields they are written in such a way that each one may be read without much reference to the other one.

In this paper we present a variant of Monkhorst’s coupled-cluster-based linear-response approach designed for direct calculations of static properties of closed-shell many-fermion systems [Int. J. Quantum Chem Symp. 11, 421 (1977)]. All the required equations are derived in the framework of the coupled-cluster singles and doubles model. Although the approach has been developed with the calculation of electric-dipole moment of atoms and molecules due to parity- and time-reversal-violating interactions in mind, it is general enough to be applicable to other problems which require the presence of two one-electron perturbations.

It is shown that the elementary indistinguishability properties of partially polarized mixtures are consistent only with the conventional Hilbert space model of quantum mechanics and a few exotic alternatives. This applies even in low dimensions where quantum logic and Gleason’s theorem give either weak or no constraints. The experimental methods for eliminating the exotic cases (which include quaternionic and octonionic variants of quantum mechanics) are described.

It is shown that provided two devices are distinguishable, their electromagnetic interactions are in essence classical. This results in the existence of simple correspondence rules connecting q- and c-number statistical descriptions of macroscopic optical arrangements. These rules allow formulas found by c-number techniques to be used as precise quantum relations. For the vast majority of real devices, including all linear devices and real light detectors regardless of their internal system, their c-number macroscopic description can be directly employed in QED. The problem of locality of QED is discussed and a rigorous theory of electrical-feedback arrangements in optics is presented.

By developing our previous method [Phys. Rev. A 46, 2337 (1992); J. Chem. Phys. 98, 543 (1993)], we show how to calculate Kohn-Sham kinetic energies, orbitals, orbital energies, and exchange-correlation potentials, starting from accurate ground-state electron densities. In addition, given correct total energies, we also show how to obtain exchange-correlation energies. The scheme used is based on the Levy constrained-search method for determining the Kohn-Sham kinetic energy. In our preferred implementation, the total electron-electron repulsion is written as a Fermi-Amaldi term plus the rest, thereby assuring the correct long-range behavior of the exchange-correlation potential. Results are given for He, Be, Ne, and Ar. It is demonstrated that the exact exchange-correlation functional cannot be local.

Measurements and calculations of the resonance between the Ly-α line of magnesium and the 2s→3p transition in neonlike germanium are presented. This resonance is of possible use as part of a resonantly photo-pumped x-ray laser scheme recently proposed which would lase on several 2p→2s transitions between 64 and 89 Å in neonlike germanium. Measurements of the resonance are made by three different approaches: one using the electron beam ion trap, the second using laser-produced plasma, and the third on a tokamak. These results are compared with calculations and other measurements. Certain discrepancies are observed with previous measurements which may be due to the partial overlap between oxygenlike and neonlike lines in germanium. The results do show a good resonance between magnesium and germanium, with the germanium line between the two Ly-α components of magnesium but nearer to the short-wavelength component.

We report measurements of transition energies for highly ionized uranium. For hydrogenic uranium we have measured 102 130±92 eV for the 2${\mathit{p}}_{3/2\mathrm{-}}$1${\mathit{s}}_{1/2}$ transition. This measurement is sensitive to the 1s Lamb shift, probing the electron self-energy in high-field QED. In addition, we have measured the (1s2p${)}^1$${\mathit{P}}_1$${,}^3$${\mathit{P}}_{2\mathrm{-}}$(1${\mathit{s}}^2$${)}^1$${\mathit{S}}_0$ transition in heliumlike uranium as 100 598±111 eV, probing relativistic electron-electron correlation effects. Both measurements were obtained with a Doppler spectrometer, a proven technique which we have adapted to the field of high-Z precision atomic transition-energy measurements. These measurements demonstrate the potential of this technique to attain ∼1 eV uncertainties.

We present a complex-coordinate rotation calculation of doubly excited ${}_{}{}^{1,3}{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ resonance states in ${\mathrm{Ps}}^{\mathrm{-}}$ associated with the N=3, N=4, and N=5 Ps thresholds. Elaborate Hylleraas-type wave functions with up to N=1330 terms are used. In addition to Feshbach resonances below various Ps thresholds, we have identified ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ shape resonances with one each lying above the N=3 and N=5 Ps thresholds, respectively, as well as a ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ shape resonance above the N=4 threshold. A physical interpretation of the doubly excited ${\mathrm{Ps}}^{\mathrm{-}}$ is also given.

Fluorescence and excitation spectra of HgCd were studied using pump-and-probe methods of laser spectroscopy with time resolution. A Hg-Cd vapor mixture, contained in a sealed quartz cell at 700 K, was irradiated by consecutive pump and probe dye-laser pulses. The pump radiation produced a population of Cd 5 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ atoms whose three-body collisions with Hg atoms resulted in the formation of HgCd excimers in the A$0^{\mathrm{-}}$, A$0^{+}$, and A1 states, correlated with the Cd 5 ${}_{}{}^3{}_{}{}^{}$P+Hg 6 ${}_{}{}^1{}_{}{}^{}$S manifold, which decayed, emitting a previously reported 4600-Å fluorescence continuum. The probe pulses, delayed by 450 ns, excited the excimers to the higher-lying C$0^{+}$ (Cd 5 ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$+Hg 6 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$) state, which decayed to the repulsive X$0^{+}$ ground state, emitting fluorescence in the 2400–2650-Å region. We also observed a bound-bound excitation spectrum in the 5800–7100-Å region. A study of the time evolution of the excimer fluorescence yielded an approximate value for the three-body rate coefficient for HgCd formation, and an analysis of the spectra produced spectroscopic constants for the states involved in the transitions.

Time-correlated single-photon counting is used to measure the lifetimes of the 6p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$ and 6p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ levels in atomic Cs with accuracies ≊0.2–0.3 %. A high-repetition-rate, femtosecond, self-mode-locked Ti:sapphire laser is used to excite Cs produced in a well-collimated atomic beam. The time interval between the excitation pulse and the arrival of a fluorescence photon is measured repetitively until the desired statistics are obtained. The lifetime results are 34.75(7) and 30.41(10) ns for the 6p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$ and 6p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ levels, respectively. These lifetimes fall between those extracted from ab initio many-body perturbation-theory calculations by Blundell, Johnson, and Sapirstein [Phys. Rev. A 43, 3407 (1991)] and V. A. Dzuba et al. [Phys. Lett. A 142, 373 (1989)] and are in all cases within 0.9% of the calculated values. The measurement errors are dominated by systematic effects, and methods to alleviate these and to approach an accuracy of 0.1% are discussed. The technique is a viable alternative to the fast-beam laser approach for measuring lifetimes with extreme accuracy.

A model with all the degrees of freedom of the core and all the radial degrees of freedom of the valence electrons frozen is used to investigate the effects of quantum-mechanical symmetry on electronic correlations of intrashell states of four-valence-electron atoms. A number of different correlative densities have been calculated. A spin-polarity-dependent analysis has been made. The emphasis is placed on the qualitative aspect. The 12 N=2 intrashell states of carbon are selected as the object of study; however, the qualitative features extracted are expected to be quite general. The morphology of each state (including the most probable shape, the most probable orientation, and the preferreed modes of internal motion) has been studied. The effect of quantum-mechanical symmetry was found to be decisive.

The binding of a single positron to a many-electron system (in the field of a fixed nuclear configuration) is viewed in terms of positron and electron densities. Following the treatments due to Levy and co-workers [Phys. Rev. A 32, 2010 (1985); 30, 2745 (1984)], certain general integral conditions and also an exact differential equation for the positron density are derived. It is demonstrated further that within a density-functional approach, decent estimates to the positron affinity for negative ions can be obtained by invoking the Slater transition state concept. Finally, the redistribution in the electron part brought about by transiently binding the positron to the negative ion is discussed at the density-matrix level.