It is suggested that the supersymmetric WKB (SWKB) method may be useful in studying the deviation of the energy levels of a quantum system due to the presence of a spherically confining boundary. For illustration, we present the explicit results for the Coulomb and three-dimensional harmonic-oscillator potentials. It is observed that the confining geometry removes the angular-momentum degeneracy of the electronic energy levels of a free atom. Our predicted energy eigenvalues are in agreement with the exact ones obtained numerically.

We study the bound states of ${\mathrm{Ca}}^{\mathrm{-}}$ based on the Brueckner approximation. We use the B-spline method to solve the Brueckner equation self-consistently. At the first iteration we obtain the energy levels of 4p states of ${\mathrm{Ca}}^{\mathrm{-}}$ which are close to those obtained by previous similar theoretical calculations. However, the bound states disappear after the first iteration in our calculation. This suggests that the existence of the bound states of ${\mathrm{Ca}}^{\mathrm{-}}$ is more subtle than previously thought.

Corrections to the energy of S levels of positronium of order m${\mathrm{\alpha }}^6$ that are as large as several hundred kilohertz are obtained. A recoil correction of order α(Zα${)}^5$(m/M)m to the Lamb shift in hydrogen is calculated. This correction turns out to be too small from a phenomenological point of view.

We have used photographic spectroscopy of a beam-foil source to perform a precision measurement of the vacuum ultraviolet 1s2s ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$-1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{2,0}$ transition wavelengths in heliumlike phosphorus. The results are 739.920±0.025 Å and 813.32±0.06 Å, respectively. This measurement constitutes a sensitive test of current relativistic and quantum electrodynamic calculations.

The method of hyperspherical ‘‘surface’’ functions has been applied to the calculation of eigenvalues and eigenfunctions of muonic molecular ions ${}_{}{}^{3,4}{}_{}{}^{}\mathrm{\mu }$. Binding energies and nonradiative decay rates for the states of the total angular momentum L=0, 1, 2 have been obtained.

From the minimal properties of the density functionals ${\mathit{T}}_{\mathit{s}}$[ρ] and F[ρ] under the constraint that the number of particles remains constant, it follows that (${\mathrm{\partial }}^2$${\mathit{T}}_{\mathit{s}}$[ρ])/[∂ρ(r)∂ρ(r’)] and (${\mathrm{\partial }}^2$F[ρ])/[∂ρ(r)∂ρ(r’)] are positive definite matrices within a well defined subspace. These general properties lead to specific inequalities satisfied by first derivatives of density functionals.

A body-frame adiabatic-nuclei rotation (ANR) calculation for ${\mathit{e}}^{+}$-${\mathrm{H}}_2^{+}$ scattering has been carried out in the energy range 0.5–10.0 eV. The j=0 to j=2 rotational excitation cross sections are reported. These results are compared with the laboratory-frame close-coupling approximation (LFCCA) results of Mukherjee et al. The present ANR results are in good agreement with those of the LFCCA above the incident positron energy of 5.0 eV.

The extended Wannier ridge model is shown to be able to reproduce the observed triple differential cross sections (TDCS) for the double-photoionization process γ+Ne(2${\mathit{p}}^6$)→${\mathrm{Ne}}^{2+}$(2${\mathit{p}}^4$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$)+e+e at a rather high excess energy E=40.6 eV. The secondary maximum in TDCS is related to the kinematic electron correlation in the initial state just as in the previously studied photoionization of Xe atoms. Variation of TDCS patterns at varying energies for Ne and Xe atom is described.

Excitation molecular oxygen has been studied in 1.8-keV collisions with projectile ions ${\mathrm{H}}_2^{+}$, ${\mathrm{N}}_2^{+}$, ${\mathrm{O}}_2^{+}$, and ${\mathrm{CO}}_2^{+}$ by means of energy-loss spectrometry. The dependence of the excitation cross section upon the quantal description of projectile ions is probed. The excitation cross section is largest in the case of collisions with ${\mathrm{H}}_2^{+}$ ions, in conformity with computed overlaps of the highest occupied molecular orbitals of the colliding systems.

We have studied a laser system in which initially incoherent atoms are injected into a cavity and directly driven by a coherent pump field. Here we show that such a system can display optical bistability in the absence of population inversion. Two disconnected branches of the solutions are obtained for lasing action. They correspond to the inversion branch and inversionless branch, respectively. Also, a mechanism is proposed here to produce higher-power lasing by the inversionless laser.

The statistics of pulse height ${\mathit{I}}_{\max }$, pulse energy A, and pulse width of gain switched semiconductor lasers are obtained for different positive and negative values of the gain saturation factor by using the linear dependence of ${\mathit{I}}_{\max }$ and A on the switch-on time.

We show that the three enigmatic lobes or petals observed in the far-field fanning pattern of photorefractive ${\mathrm{BaTiO}}_3$ crystals are correctly predicted by considering the piezoelectric and photoelastic contributions of crystal deformations to the photorefractive nonlinearity.

A simple quon gas model which interpolates between the boson gas and the fermion gas is proposed. The fermion limit is realized without use of the exclusion principle. The second and third virial coefficients are calculated and compared with those of a free anyon gas. If the fugacity is small the system can simulate an anyon gas which has the Maxwell-Boltzmann limit.

Ermakov systems are pairs of coupled, time-dependent nonlinear dynamical equations possessing a joint constant of motion. We show how to derive the Ermakov system from nonharmonic oscillators. We present a detailed study of Ermakov systems from a classical and quantum point of view. Finally the nonadiabatic Hannay’s angle and Berry’s phase for the system are calculated along with its adiabatic limit.

Using the exact realization of the Morse oscillator problem in terms of SO(2,1) symmetry and its bosonization, the corresponding q deformation is performed. The ground-state energy is found to remain constant for all arbitrary (zero, real, imaginary, or complex) values of the q-deformation parameter. By fitting the resulting q-deformed energy-level spectrum to data for the hydrogen molecule in its ground electronic state, it is shown that, depending upon the value of the scaling constant, a considerable improvement results for the real and/or imaginary q deformation over the corresponding result for the classical Morse oscillator, and that the best fit is obtained in the q-deformed case with a complex value of the deformation parameter.

A method is presented for the construction of Wentzel-Kramers-Brillouin (WKB) wave functions that avoids explicit consideration of any matching between results pertaining to classically allowed and forbidden regions. The formalism is based on the maximization of a suitable defined quantal pseudoentropy, subject to the constraints posed by the expectation values of a reduced number of operators, which are evaluated according to special WKB techniques. A self-consistent procedure is developed that simultaneously yields the nodes of the wave function and the information theory parameters.

Corrections to the hyperfine splitting and the Lamb shift of order ${\mathrm{\alpha }}^2$(Zα${)}^5$ induced by diagrams with radiative photon insertions in the electron line are calculated in the Fried-Yennie gauge. These contributions are as large as -7.724(1)${\mathrm{\alpha }}^2$(Zα${)}^5$/(π${\mathit{n}}^3$)(${\mathit{m}}_{\mathit{r}}$/m${)}^3$m and -0.6726(4)${\mathrm{\alpha }}^2$(Zα)/(π${\mathit{n}}^3$)${\mathit{E}}_{\mathit{F}}$ for the Lamb shift and the hyperfine splitting, respectively. Phenomenological implications of these results are discussed with special emphasis on the accuracy of the theoretical predictions for the Lamb shift and the experimental determination of the Rydberg constant. A precise value of the Rydberg constant is obtained on the basis of the improved theory and experimental data.

We present basis-set Dirac-Fock calculations of the ground states of the ${\mathrm{H}}_2$, HF, HCl, ${\mathrm{H}}_2$O, ${\mathrm{NH}}_3$, and ${\mathrm{CH}}_4$ molecules. Molecular orbitals are constructed by linearly combining four-component spherical spinors centered at the nuclei; the radial dependence of the large component is ${\mathit{r}}^{\mathit{n}}$${\mathit{e}}^{\mathrm{-}\xi \mathit{r}2}$, where n is a non-negative integer determined by the angular quantum numbers, and ξ∈a,ab,${\mathit{ab}}^2$,..., where a>0 and b>1 are real numbers; the small component is generated from the large component using the ‘‘strict kinetic balance’’ prescription. Our estimates of the ground-state energies of these molecules decrease monotonically as the size of the basis sets used is enlarged. The nonrelativistic (essentially basis-set Hartree-Fock) limits of our calculations are obtained by increasing the speed of light by a few orders of magnitude over its physical value; we are thus able to estimate relativistic corrections in an unambiguous way within the context of our molecular models.

Various density-functional relations are established involving functional expansions for quantities of interest. The central identity expresses an arbitrary well-behaved functional F[ρ] in terms of the actual density ρ(x) and the functional derivatives of F[ρ] evaluated at the density ρ(x). A number of useful consequences of the formulas are given.