We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A 31, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical systems possessing Lie-group symmetries. The concept of generalized coherent states and the method of harmonic analysis are used to construct explicitly a family of phase-space functions which are postulated to satisfy the Stratonovich-Weyl correspondence with a generalized tracing condition. The symbol calculus for the phase-space functions is given by means of the generalized twisted product. The phase-space formalism is used to study the problem of the reconstruction of quantum states. In particular, we consider the reconstruction method based on measurements of displaced projectors, which comprises a number of recently proposed quantum-optical schemes and is also related to the standard methods of signal processing. A general group-theoretic description of this method is developed using the technique of harmonic expansions on the phase space.

This paper presents analytic formulas for various transition times in the Landau-Zener model. Considerable differences are found between the transition times in the diabatic and adiabatic bases, and between the jump time (the time for which the transition probability rises to the region of its asymptotic value) and the relaxation time (the characteristic damping time of the oscillations which appear in the transition probability after the crossing). These transition times have been calculated by using the exact values of the transition probabilities and their derivatives at the crossing point and approximations to the time evolutions of the transition probabilities in the diabatic basis, derived earlier [N. V. Vitanov and B. M. Garraway, Phys. Rev. A 53, 4288 (1996)], and similar results in the adiabatic basis, derived in the present paper.

In terms of the modified Sturm-Liouville theorem, the two-dimensional Levinson theorem for the Klein-Gordon equation with a cylindrically symmetric potential $V\left(r\right)\mathrm{}$ is established for an angular momentum m as a relation between the numbers $n_m^{\pm }$ of the particle and antiparticle bound states and the phase shifts ${\eta }_m(\pm M):$ ${\eta }_m\mathrm{}\left(M\right)\mathrm{}-{\eta }_m\left(-M\right)=\{\{{(n}_m^{+}-n_m^{-}+1)\pi \hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em},\mathrm{when}\mathrm{}\mathrm{a}\mathrm{}\mathrm{h}\mathrm{a}\mathrm{l}\mathrm{f}-\mathrm{b}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}\mathrm{}\mathrm{state}\mathrm{}\mathrm{occurs}\mathrm{}\mathrm{at}\mathrm{}E=M\hspace{0.5em}\hspace{0.5em}\mathrm{for}\hspace{0.5em}\hspace{0.5em}m=1\mathrm{}\left\}\right\{{(n}_m^{+}-n_m^{-}-1)\pi \hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em},\mathrm{when}\mathrm{}\mathrm{a}\mathrm{}\mathrm{h}\mathrm{a}\mathrm{l}\mathrm{f}-\mathrm{b}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}\mathrm{}\mathrm{state}\mathrm{}\mathrm{occurs}\mathrm{}\mathrm{at}\mathrm{}E=-M\hspace{0.5em}\hspace{0.5em}\mathrm{for}\hspace{0.5em}\hspace{0.5em}m=1\mathrm{}\}\left\{{(n}_m^{+}-n_m^{-}\right)\pi \hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em}\hspace{0.5em},\mathrm{the}\mathrm{}\mathrm{remaining}\mathrm{}\mathrm{cases}.\mathrm{}\mathrm{}\}$ A solution of the Klein-Gordon equation with the energy M or $-M$ is called a half-bound state if it is finite but does not decay fast enough at infinity to be square integrable.

Periodic orbit expressions for the density of states lead to spurious results when directly used to calculate quantities of thermodynamic interest. This is because the trace formula is usually valid only for large energies, while the calculations make use of it at all energies. We present a prescription for circumventing this problem by isolating contributions that arise from the inaccurate low-energy behavior, and that are spurious, from other subdominant contributions that are physical and are not contained in the Weyl series. The method is tested by analyzing the fermionic grand partition function for a disk billiard, and may readily be extended to other dynamical systems.

We have calculated the $O\left(\alpha \right)$ radiative correction affecting the decay rate of parapositronium to four photons. Our result for the rate is $\Gamma \left(4\mathrm{}\gamma \right)={\Gamma }_{\mathrm{LO}}\left(4\mathrm{}\gamma \right)\left[1-14.5\right(6)\mathrm{}\alpha /\pi +O({\alpha }^2\left)\right],$ where ${\Gamma }_{\mathrm{LO}}\left(4\mathrm{}\gamma \right)$ is the lowest order four-photon decay rate. Our prediction for the four-photon to two-photon branching ratio, including all $O\left(\alpha \right)$ corrections, is $R=1.4388\mathrm{}\left(21\right)\mathrm{}\times {10}^{-6}.$ We also have a higher precision result for the lowest-order rate: ${\Gamma }_{\mathrm{LO}}\left(4\mathrm{}\gamma \right)=0.013\mathrm{}8957\left(4\right)m{\alpha }^7.$

A very accurate variational expansion is suggested for calculation of nonrelativistic energies of the metastable antiprotonic helium atoms ${\mathrm{He}}^{+}\overline{p}.$ This expansion reflects the dual atomic-molecular nature of the system. Convergence of the results as a function of the increasing sets of basis functions shows an accuracy better than ${10}^{-10}\mathrm{a}.\mathrm{u}.\mathrm{},$ two orders of magnitude better than in our previous calculations.

We carry out state-selective Rabi and Ramsey magnetic-resonance experiments on ground-state ${}^{133}\mathrm{Cs}(\mathrm{F}=4\mathrm{})$ atoms. Novel line shapes are obtained, which exhibit very sharp features with a width much smaller than the inverse duration of the magnetic-resonance pulse. The sensitivity of ordinary magnetic-resonance experiments with total spin $\mathrm{F}\mathrm{}>1/2\mathrm{}$ is significantly less than the Heisenberg limit, which can be exactly realized only with maximally correlated spin states. We show that the state-selective resonances yield sensitivity very close to the Heisenberg limit, without any state preparation beyond ordinary optical pumping.

The $2\overrightarrow{p}ns,md$ excitation spectrum has been measured and calculated for the open-shell Cl atom. A satisfactory accord between experiment and theory was found. Rydberg series cannot be discerned for transitions leading to a $2p,$ $3p,$ $n\mathcal{l}$ open-shell configuration. The $4s,3d$ manifolds are dominant, and the $2p-3p$ coupling is seen to be much stronger than the $3p-n\mathcal{l}$ coupling. Very narrow widths, 16 to 22 meV, for the $4s$ and $3d$ lines are observed. By contrast, only broad structures appear in the region of the highest excitations.

Weakly dipole-bound electron systems having large wide-ranging zero vibrational effects often exhibit large discrepancies between theory and experiment. The present study utilizing a quantum-mechanical probabilistic approach characterizes the structure of the anionic water dimer $[e+({\mathrm{H}}_2\mathrm{O}{)}_2]$ (one of the most weakly dipole-bound electron systems) as linearlike, slightly towards the cis conformer at 0 K. The resulting electron detachment energy, adiabatic electron affinity, and the deuteration effect of the predicted structure are in good agreement with experimental results.

We have succeeded in magneto-optical trapping of Yb atoms decelerated by a Zeeman slower method. The number of the trapped atoms is more than about $1.3\times {10}^6$ measured by light absorption. We have found the evidence of the branching from the ${}^1{P}_1$ excited state to triplet states, and determined the lower limit on the branching ratio to be $1.2\times {10}^{-7}.$

Bose-Einstein condensation of ${}^{87}\mathrm{Rb}$ has been observed in a vapor cell time-averaged orbiting potential trap, and the trapped condensates have been studied using in situ absorption and dark-ground imaging methods. Condensates of $3\times {10}^4$ atoms were observed after 26 s of evaporative cooling. The evaporative cooling sequence consisted of a combination of cooling with ramping magnetic-field strengths and radio-frequency-induced cooling. The measured sizes, numbers of atoms, and transition temperatures of the condensates are consistent with theoretical predictions that include the effects of atomic interactions.

We describe a method for measuring the forward-scattering amplitude for electron collisions with atoms or molecules. Our scheme uses a gas cell in one arm of an electron interferometer and measures the resulting attenuation and phase shift of the electron matter wave. The complex index of refraction of the gas is determined along with the forward-scattering amplitude. Calculations of the scattering of electrons by atoms are performed using a self-energy potential obtained by treating the atom as an inhomogeneous electron gas. The results indicate that the proposed experiments are feasible.

Possibilities of elimination of Doppler broadening by making use of atomic coherence in ladder- and folded-type configurations of quantum transitions are considered. A simple physical analysis in terms of modification of the frequency-correlation factor for cascade and multiphoton processes in strong driving fields is developed.

We present a simple and fast scheme to measure the state of a trapped atom. Our method directly yields the characteristic function of the Wigner function avoiding a demanding data analysis. We show that our method can be readily applied to an actual experiment.

Using the large-order formula for the coefficients of the divergent weak-coupling series for the energy of the anharmonic oscillators, we derive a simple analytic large-order formula for the coefficients of the convergent renormalized strong-coupling series. This formula is valid for all the states of the anharmonic oscillators defined by the Hamiltonians ${H=p}^2{+x}^2+\beta x^{2m}$ with $m>~2.$ A further generalization of this formula is also proposed. Numerical tests of the formula are performed for the quartic, sextic, octic, and decadic oscillator with the help of asymptotic analysis. Further it is shown that the renormalized strong-coupling perturbation expansion converges for all the states of these oscillators and for all physically relevant $\beta \in [0,\infty ).\mathrm{}$

The one-dimensional Schrödinger equation, derived from the general form of the effective-mass Hamiltonian ${(m}^{\eta }\mathbf{p}{m}^{\epsilon }\mathbf{p}{m}^{\rho }{+m}^{\rho }\mathbf{p}{m}^{\epsilon }\mathbf{p}{m}^{\eta })/4+V$ with $\eta +\epsilon +\rho =-1,$ is solved exactly for a system with smooth potential and mass step. The wave function depends on the Heun function, which is a generalization of the hypergeometric function. The effective-mass Hamiltonian and the connection rules for a system with abrupt heterojunction are deduced from the study of the limiting case when the smooth step potential and mass tend to an abrupt potential and mass step.

I show a situation of multiparticle entanglement which cannot be explained in the framework of an interpretation of quantum mechanics recently proposed elsewhere. This interpretation is based on the assumption that correlations between subsystems of an individual isolated composed quantum system are real objective local properties of that system.

Recent experimental results and proposals towards implementation of quantum teleportation are discussed. It is proved that reliable (theoretically, 100% probability of success) teleportation cannot be achieved using the methods applied in recent experiments, i.e., without quantum systems interacting with one another. Teleportation proposals involving atoms and electromagnetic cavities are reviewed and the most feasible methods are described. In particular, the language of nonlocal measurements has been applied; this language has also been used for presenting a method for teleportation of quantum states of systems with continuous variables.

Stapp [Am. J. Phys. 65, 300 (1997)] has recently argued from a version of the Hardy-type experiments that quantum mechanics must be nonlocal, independent of any additional assumptions such as realism or hidden variables. I argue either that his conclusions do not follow from his assumptions or that his assumptions are not true of quantum mechanics and can be interpreted as assigning an unwarranted level of reality to the value of certain quantum attributes.

The radiation reaction fields are calculated for an accelerated changing dipole in scalar and electromagnetic (em) radiation fields. The radiation reaction is shown to alter the damping fields of a time varying dipole in the em case, but not the scalar case. In both cases the radiation reaction field can exert a force on an accelerated monopole and also on a pure accelerated dipole. The radiation reaction of an accelerated charge does not exert a torque on an accelerated magnetic dipole, but an accelerated dipole does exert a force on the charge. The technique used is that originally developed by Penrose for nonsingular fields and by the author for an accelerated charge.