The statistical operators of those isolated nonrelativistic quantum systems that are presumed to exhibit intrinsically irreversible evolutionary behavior are shown to be capable of undergoing only discontinuous changes that occur at successive instants of time that are suggestive of possible temporal discreteness and that result in ‘‘mixed-state’’ conditions of the systems. Presuming such discrete temporal structure, a temporally asymmetric difference equation is derived for these statistical operators that suffices to imply their irreversible discontinuous evolution and from which both predictability and retrodictability of their temporal behavior are possible, but the latter cannot be extended indefinitely into the past.

The two-center shell potential is an example of a system that does not possess an obvious classical analog. We carry out a detailed study of the spectral measures and find, apart from other interesting details, a regular-irregular-regular transition in both the nearest-neighbor-spacing distribution as well as the spectral rigidity with a variation in the separation between the two nuclei. Moreover, the saturation of the spectral rigidity, together with an accurate prediction of its onset using the Fourier transform of the spectrum, clearly indicates that a ‘‘Gutzwiller-like’’ sum rule for the density of states does exist in this system.

The perturbed-ladder-operator method is applied to the analytical solution of the harmonic-oscillator eigenequation perturbed by a symmetric potential V(x). This method, well adapted for computer algebra, is an extension of the original Schrödinger-Infeld-Hull factorization method within the perturbative scheme and allows an analytical solution of nonfactorizable Sturm-Liouville eigenequations in almost the same way as factorizable ones. Closed-form expressions of the perturbed harmonic-oscillator eigenvalues are obtained by means of a few algebraic manipulations, either in a series of binomial functions ${(}_{\mathit{u}}^{\mathit{v}}$) or in a series of powers (v+1/2${)}^{\mathit{u}}$. Alternative expansions of the perturbed potential V(x) in a series of Hermite polynomials ${\mathit{scrH}}_{2\mathit{s}}$(x) or in a series of ${\mathit{x}}^{2\mathit{s}}$ are considered and some illustrative examples demonstrating the capabilities of the method are given. Particularly, analytical expressions of the ${\mathit{x}}^4$-perturbed harmonic-oscillator energies, as well as analytical approximations of the eigenenergies for the ${\mathit{x}}^2$+λ${\mathit{x}}^2$/(1+${\mathit{gx}}^2$) interaction, are quickly derived.

It is demonstrated that semiclassically both the self-reaction and electromagnetic field fluctuations satisfy the condition that the field acting upon the electron is that due to its own charge and current fluctuations. The electron-field interaction energy can be found using the fluctuation-dissipation theorem, and equals 1/2ħ multiplied by the sum of the frequency shifts as in the theory of dispersion forces. For an atom in an excited state, the self-consistently obtained frequencies have an imaginary part for ħkc approximately equal to the atomic energy-level differences, giving spontaneous emission. Since the fields are real, the physically correct or Hermitian separation into self-reaction and electromagnetic contributions is obtained.

Two different mechanisms for the wave-function collapse represented by the disappearance of the off-diagonal terms in a density matrix are investigated from the viewpoint of a change of entropies in detectors by using a simple calculable model. In the mechanism called quantum collapse, the difference between the entropy of the initial detector state and that of the final one becomes a macroscopic value in the macroscopic limit where the collapse is realized, while there is no such difference in the other mechanism called pure statistical collapse, induced by thermal fluctuations of active particle numbers in detectors. We also show that in a thermodynamical limit the entropy difference logarithmically diverges in the quantum collapse. Such a change is possibly detectable in mesoscopic phenomena and the two mechanisms can be discriminated from each other by using these phenomena.

A quantum system with the Hamiltonian and commutation relations depending on a deformation parameter ε is introduced. When ε=0 the system reduces to the quantum Ablowitz-Ladik (QAL) equation, for ε=γ/3 it represents a quantum discrete nonlinear Schrödinger (QDNLS) system, and for ε=γ the system reduces to the usual QDNLS equation. We show that the energy levels of this system can be continuously deformed into the corresponding ones of the QAL and QDNLS equations. The physical significance of this system is also discussed.

A simple proof is given of a recent claim [P. Pearle, Phys. Rev. A 39, 2277 (1989)] that appropriately coupled classical white noise reduces wave packets of macroscopic objects. Three difficulties with the classical mechanism are noted. All three are resolved by passing to the quantum analog. The 2.7-K microwave background is effective in some cases. Quantum noise reduces the density matrix of observables, not the wave function itself. The relative merits and liabilities of these two kinds of reduction, called von Neumann reduction and Heisenberg reduction, respectively, are discussed. In this connection a new type of correlation experiment, devised by Hardy [Phys. Rev. Lett. 68, 2981 (1992)] is used to prove a theorem that says, essentially, that any ontological solution of the quantum measurement problem must admit either parallel worlds of the Everett kind or faster-than-light influences of some kind.

Using a supersymmetric path-integral formulation, we give explicit point canonical transformations which map the kernels (or energy-dependent Green’s function) of exactly known solvable shape-invariant potentials into those of two potential classes. Exact analytic expressions for the eigenvalues and eigenfunctions of these two classes of potentials are then retrieved following a standard procedure.

We present methods for utilizing the unitary-group approach to many-electron systems as a basis for performing variational calculations using Hylleraas coordinates. We discuss the construction of wave functions and evaluation of operator matrix elements for both spin-independent and spin-dependent interaction types.

A key process in muon-catalyzed fusion is the deexcitation of dtμ within the resonant muonic quasimolecule (dtμ)dee, by emission of an Auger electron. The dtμ in the quasimolecule is initially in a weakly bound excited state with J=1 and v=1. Calculations are carried out of the rate of the dominant transition to the state with J=0 and v=1. Use is made of the dipole matrix element obtained for this transition by Scrinzi and Szalewicz [Phys. Rev. A 39, 2855 (1989)]. Full account is taken of the molecular nature of the quasimolecule. The continuum electronic wave functions for the Auger electron for all four contributing symmetries, i.e., ${\mathrm{\Sigma }}_{\mathit{g}}^{+}$, ${\mathrm{\Sigma }}_{\mathit{u}}^{+}$, ${\mathrm{\Pi }}_{\mathit{u}}$, and ${\mathrm{\Pi }}_{\mathit{g}}$, are first obtained by a two-center Coulomb calculation and a static-exchange calculation, extended to include dipole polarization. Comparison is then made with the results of a calculation in which the ${\mathrm{\Sigma }}_{\mathrm{\mu }}^{+}$ and ${\mathrm{\Pi }}_{\mathit{u}}$ wave functions are obtained as in a previous paper by Armour and Lewis [J. Phys. B 23, L25 (1990)] and the ${\mathrm{\Sigma }}_{\mathit{g}}^{+}$ and ${\mathrm{\Pi }}_{\mathit{g}}$ wave functions are obtained by the Kohn method. There are significant differences between the contributions from the individual symmetries, but the overall values for the deexcitation rate are all of the same order of magnitude as the results of earlier calculations.

Deuteron polarization in a dμ atom and triton polarization in a tμ atom were investigated on the basis of a three- (four-) body model of the d-μ (t-μ) system. Virtual excitation of the deuteron and triton is treated within the second-order perturbation theory. The nuclear polarization energy is obtained as -9.9 meV for the dμ atom and -1.1 meV for the tμ atom. We examined the validity of the adiabatic approximation and the dipole approximation which were employed in the literature calculation of the deuteron polarization; the approximations were found to be rather poor. Deuteron and triton polarization potentials were derived and were found to deviate much, in the internal region, from the ${\mathit{r}}^{\mathrm{-}4}$-type potential, which is given by the adiabatic and dipole approximations. With the use of these potentials, correction to ${\mathrm{\epsilon }}_{11}$ due to the nuclear polarization in the dtμ molecule at the J=v=1 state was calculated to be -1.7 meV, which should significantly affect the resonant formation of the state, a key to the muon catalyzed d-t fusion.

Direct solution of the Schrödinger equation for the ground and excited S states of the μdt molecular ion is obtained with the help of the correlation-function hyperspherical-harmonic method. Given the proper correlation function, chosen from physical considerations, the method generates wave functions, accurate in the whole range of interparticle distances, which lead in turn to precise estimates of the expectation values of the Hamiltonian and of different functions of interparticle distances. Our results are compared with those obtained in other precision calculations.

The method of factorization, together with the hypervirial theorem, is shown to be appropriate for calculating matrix elements of operators that are functions of r, between hydrogenic radial wave functions that may belong to different atoms. Some numerical results are tabulated for matrix elements of the form 〈n’l’‖${\mathit{r}}^{\mathit{k}}$‖nl〉. The expressions given are valid for both diagonal- and off-diagonal matrix-element calculations with no limitation on the values of the n and l quantum number or in the power of the operator, which can have either positive or negative values.

The nonrelativistic energies of the lithiumlike 1${\mathit{s}}^2$ns (n=3, 4, and 5) states for Z=3 to 10 are calculated by using a full-core-plus-correlation method with multiconfiguration-interaction wave functions. Relativistic and mass-polarization effects on the energy are evaluated as the first-order perturbation corrections. The quantum-electrodynamic (QED) correction to the energy is included using effective nuclear charge. Our results are compared with the experimental data in the literature. For Z<8 systems, the discrepancies are about 1 ${\mathrm{cm}}^{\mathrm{-}1}$ or less in most cases. Our nonrelativistic energies are also compared with previous theoretical results in the literature.

Roothaan-Hartree-Fock self-consistent-field (SCF) kinetic energies are compared with kinetic energies obtained from various functionals applied to the SCF electron densities for a set of 77 molecules. The best functionals are much better than the second-order gradient expansion but need further improvement by an order of magnitude before they can be considered reliable for practical applications to atoms and molecules. Some suggestions are made as to how such functionals might be found.

The influence of dephasing processes on the motion of self-localized quasiparticles in molecular chains is studied within a density-matrix description. Applying the so-called self-trapping approximation, the strong coupling to vibrational degrees of freedom can be taken into account by a quadratic nonlinearity in the density-matrix equations. If dephasing is neglected, the results agree well with those of the so-called ${\mathit{D}}_2$ ansatz in the theory of Davydov solitons. The delicate dependence of the soliton formation on the employed particle-vibration coupling is demonstrated. Using the standard model for the exciton motion in α-helical structures of polypeptides, it is shown that the soliton motion over more than ten molecules in the chain requires a dephasing time below some hundred femtoseconds. Thus the soliton mechanism of energy transport in biological systems at physiological temperatures seems very improbable.

The two-electron Schrödinger equation is analyzed in hyperspherical coordinates, with the electrons described throughout as a pair. In contrast to the current adiabatic hyperspherical method, which reverts at large distances to a description in terms of individual electrons, the pair aspect is preserved also asymptotically. Whereas the adiabatic potential wells converge to single-ionization limits, we develop potential wells converging to the double-ionization limit of the system, and doubly excited states are then viewed as eigenstates of the pair in these wells. At the simplest level, we get series converging to the double-ionization limit which are described analytically by the ‘‘pair-Rydberg’’ formula, with an effective charge that increases logarithmically with the principal quantum number.

The relative photodetachment cross section for decay into the H(N=2) channel by the ${}_{}{}^1{}_{}{}^{}$P° shape resonance in ${\mathrm{H}}^{\mathrm{-}}$ was measured, as well as that for decay into all channels. The branching ratio σ(N=2)/σ(total) was computed for a series of energies between 10.95 and 11.3 eV after normalizing the cross sections to theoretical peak amplitudes. The maximum branching ratio (≊0.8) appears at an energy about 20 meV higher than the central energy of the resonance. Results are compared with recent theoretical calculations.

Electron elastic and collisional excitation cross sections from the ground state of potassium are calculated using the noniterative integral-equation method of Henry, Rountree, and Smith [Comput. Phys. Commun. 23, 233 (1981)] in the electron energy range 4≤E≤200 eV. Configuration-interaction target wave functions that take account of correlation and polarization effects are used to represent the ground state and the six lowest excited states 4p ${}_{}{}^2{}_{}{}^{}$P°, 5s ${}_{}{}^2{}_{}{}^{}$S, 3d ${}_{}{}^2{}_{}{}^{}$D, 5p ${}_{}{}^2{}_{}{}^{}$P°, 4d ${}_{}{}^2{}_{}{}^{}$D, and 6s ${}_{}{}^2{}_{}{}^{}$S. Elastic and discrete excitation cross sections are obtained in a seven-state close-coupling (7CC) approximation. The 7CC elastic and excitation cross sections are compared and contrasted. Near threshold the elastic cross section dominates the resonance, 4s ${}_{}{}^2{}_{}{}^{}$S→4p ${}_{}{}^2{}_{}{}^{}$P°, and the sum of the other remaining excitation cross sections. Comparison of our total cross sections with some available experimental and theoretical data is also effected. The discrepancy between the recent measurement of the total cross section by Kwan et al. [Phys. Rev. A 44, 1620 (1991)] on the one hand and other measurements near threshold on the other hand is explained.

The elastic scattering of two hydrogen atoms interacting at very small energies is explored numerically using the most accurate potential-energy curves available for the X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ states of ${\mathrm{H}}_2$. The scattering lengths and low-temperature-averaged cross sections are determined and compared with previous calculations. The scattering lengths are 0.41${\mathit{a}}_0$ for the singlet case and 1.91${\mathit{a}}_0$ for the triplet. The predicted total triplet cross section at 2 K is 5.5×${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$ but it could be lower, at 4.8×${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$, with a different fit to the triplet potential between 12${\mathit{a}}_0$ and 15${\mathit{a}}_0$. A more accurate triplet-state potential is needed at these separations.