It is well known that bound states cannot be obtained by Rayleigh-Schrödinger or Wigner-Brillouin perturbation theories. Here we apply a recently developed perturbation theory to the hydrogen atom, treating the full Coulomb potential as a perturbation. In first order we obtain a correction to the well-known Lifshitz method. The third order gives almost the exact result.

An algebraic approach to obtain ladder operators for hydrogenlike wave functions from the algebraic representation of the ${\mathit{L}}_{\mathit{n}}^{\mathit{k}}$ Laguerre associated polynomials directly involved is presented. The method leads to diverse ladder operators depending on the manner as the operational form of ${\mathit{L}}_{\mathit{n}}^{\mathit{k}}$ is used. As an example, this work deals with linear creation and annihilation operators of two kinds: some that influence the n energy quantum number and others acting on the l orbital number according to usual ladder properties. In addition, as a useful application of the raising and lowering operators thus obtained, generalized recurrence relations and closed formulas for the calculation of multipole matrix elements are algebraically deduced by means of a procedure that takes advantage of the relationship between the ladder operators associated with the bra and those related to the ket.

We consider how a class of realistic models in which an individual system, while undergoing transitions, is at any instant definitely in one or the other state can mimic the prediction of quantum theory for two-state oscillations. We show explicitly the way in which the measurement must be invasive for such models, even at the microscopic level.

We propose a solution to the problem of solving the Schrödinger equation for an arbitrary number of identical one-dimensional harmonically coupled oscillators raised by Fan Hong-yi [Phys. Rev. A 42, 4377 (1990)]. The relationship between the Fock spaces associated with the uncoupled and coupled oscillators is given as well as the coordinate representation of the eigenstates. In view of further applications, the Lie algebraic properties of the model are examined, and the generalization to three spatial dimensions is made.

Principal-axis hyperspherical coordinates (made up of one hyperradius and 3N-7 angles as internal coordinates) and three Euler angles as external (rotational) coordinates [X. Chapuisat and A. Nauts, Phys. Rev. A 44, 1328 (1991)], are used to describe an N-particle system. The exact quantum-mechanical Hamiltonian of the system in terms of these coordinates is established and is very simple. Generalized angular-momentum vector operators, which allow the generation of a profitable standard representation for the angular part of the problem, are introduced. The corresponding matrix representation of the Hamiltonian operator is built.

The four-velocity and orientation of an ‘‘elementary’’ particle is given classically by the Lorentz transformation from the rest frame of the particle to the observer’s frame. This transformation, first discussed in detail by Gürsey [Nuovo Cimento 5, 784 (1957)], is the classical eigenspinor of the particle; it is shown here to satisfy a trivial four-momentum relation that is the exact analog of the Dirac equation of relativistic quantum theory. Although the classical elementary particle can spin at an arbitrary rate, it is constrained by the Lorentz-force equation and by the linearity of its time evolution to have a g factor of 2. Bilinear covariants of its eigenspinor include the four-velocity and spin, and these as well as the transformations of the eigenspinor under P, T, and C, have the same form as in quantum theory. However, the bilinear covariants giving the spacelike Frenet vectors orthogonal to the spin have no counterparts among the usual bilinear covariants ψ¯Γψ of quantum theory, although they can be expressed in the form ψ¯Γ${\mathrm{\psi }}^{\mathit{c}}$, where Γ is a sum of products of Dirac matrices and ${\mathrm{\psi }}^{\mathit{c}}$ is the charge-conjugated spinor wave function. The relation of the classical and quantum theories is strengthened by a discussion of the superposition of eigenspinors and the eigenspinor field of a classical distribution of particles.

We show that the quantum group ${\mathrm{SU}}_{\mathit{q}}$(2) can be realized in a classical symmetric-top system as long as a suitable Hamiltonian and symplectic structure are chosen. The usual Lie group can be recovered when the deformation parameter q equals 1. The Hamiltonian system in which the quantum group is realized obeys the same equations of motion with the standard Hamiltonian system, but these two Hamiltonian systems have different constants of motion that reflect that the symmetries are different.

Intermediate-range ‘‘high-frequency’’ electromagnetic interaction between varying-sized mesoscopic chunks of semicondensed electrically neutral matter favors spatial clustering of larger chunks into ‘‘isolated’’ macroscopic systems. A complementary aspect of QED provides, via lower-frequency coherent states (with a classical-radiation interpretation) and the Raman effect, quantum-mechanical meaning for ‘‘awareness of surroundings’’ by isolated macroscopic systems.

We analyze and propose a method to detect the Aharonov-Bohm effect due to time-varying vector potentials, specifically those arising from a coherent light source. We show that the effect is feasible for use as a light-intensity detector. The quantum limit of detection is that of a single photon. Such a system would be a quantum-nondemolition measurement since no photon absorption occurs.

We derive an extended expression of the density of states for Hamiltonian chaos in the present paper and will discuss the possibility of explicit construction of the quantization condition for chaos in a future article. In view of the controversial validity of Gutzwiller’s density of states, we apply our phase-space semiclassical mechanics [K. Takatsuka, Phys. Rev. Lett. 61, 503 (1988); Phys. Rev. A 39, 5961 (1989)] in order to construct independently the expression for both regular and irregular spectra in a unified manner. It is shown that the Liapunov exponent, Greene’s residue in classical chaos, and the Maslov index in the Einstein-Brillouin-Keller conditions are closely related to each other through the amplitude factor of our phase-space kernel. In particular, the Maslov index is interpreted as a quantum-mechanical phase due to the spinning motion of a volume element that is to be carried by a phase flow along a periodic orbit. The difficulty in semiclassical mechanics is argued in terms of the exponential decay of a time correlation function. Furthermore, a formal aspect of the thermodynamic characterization of quantum chaos is addressed, defining the dynamical temperature and entropy through the analytic structure of the density of states.

The derivation from a relativistic field theory of equations describing two interacting particles has, in the past, been based on the study of the matrix element of a product of field operators taken between a two-particle state and the vacuum. Instead, we propose here to study the matrix element of a single field operator connecting a two-particle state to a one-particle state; this introduces an asymmetry between the particle that is on and the one that is off the mass shell. We derive an equation for fermions that in the infinite-mass limit for the particle on the mass shell goes over into the correct (Dirac) equation for the light particle moving in the external field generated by the heavy one. For the equal-mass case, we show how symmetry between the two particles can be restored and a useful equation obtained at the level of approximation involving one-boson exchange and suppression of negative-energy intermediate states. The calculations are carried through for QED in the radiation gauge.

An analysis of the motion of a classical charged particle in its self-field is carried out. The original study of Dirac in 1938 [Proc. R. Soc. London, Ser. A 167, 148 (1938)] made use of the energy-momentum tensor to conclude that the retarded minus the advanced fields must be used in the limit onto the source. In this paper, a criterion based on the vanishing of the total force on an uncharged system is used to arrive, in quite a different way, at the same formula. Some insights are provided by this method. It is shown that there is a basic inconsistency in this construction for the case of a two-body system with zero net charge if the two masses are not equal. Application of Dirac’s formula to the unequal-mass case results in the same inconsistency. The case of the massless charged particle is also considered.

A quantum-mechanical measurement process is analyzed in terms of a model Hamiltonian describing the interaction between a quantum system (a ‘‘particle’’) and a macroscopic apparatus (a ‘‘detector’’), which is assumed to be made up of N two-level elementary constituents (‘‘molecules’’). The description of the molecule locations introduces an effective fluctuating coupling constant, and this provokes a loss of quantum-mechanical coherence in the limit of large N. It is argued that coherence is lost statistically, as a result of the interaction: The collapse of the wave function is indeed obtained when the same experiment is performed many times, as a result of the microscopic differences among macroscopically identical initial states of the detector. In this way, insight is obtained into the mechanism engendering the loss of coherence suffered by a quantum-mechanical system when interacting with a macroscopic apparatus, and the concept of ‘‘wave-function collapse’’ is replaced by that of a statistically defined dephasing process. No classical behavior of the detection system is postulated and the presence of no external observer is required.

Excitation energies and oscillator strengths from the ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ ground state to the first ${}_{}{}^1{}_{}{}^{}$P${\mathrm{°}}_1$ and ${}_{}{}^3{}_{}{}^{}$P${\mathrm{°}}_1$ excited states of Zn-like ions are calculated by using the multiconfiguration relativistic random-phase approximation. Results are compared with those from other theories and with experiment. Predicted values for highly stripped ions are listed.

High-resolution He i and He ii excited inner-valence photoelectron spectra of the oxygen molecule have been recorded between 20 and 26 eV. In this range three photoelectron bands are clearly observed that are associated with transitions to the ${\mathit{B}}^2$${\mathrm{\Sigma }}_{\mathit{g}}^{\mathrm{-}}$, ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathit{u}}^{}{}_{}{}^{}$, and ${\mathit{c}}^4$${\mathrm{\Sigma }}_{\mathit{u}}^{\mathrm{-}}$ cationic states. Vibrational structure is observed in all photoelectron bands, and the vibrational constants have been determined. The rotational profile of the vibrational lines is resolved for the B state, and an analysis is made in terms of transitions involving ΔN=0 and ±2. In addition to the three strong bands, a fourth, weak vibrational progression has been observed in the range of the ${\mathit{B}}^2$${\mathrm{\Sigma }}_{\mathit{g}}^{\mathrm{-}}$ state. The state of ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathit{u}}^{}{}_{}{}^{}$ symmetry observed around 24 eV shows a long vibrational progression with spacings that decrease successively towards higher electron binding energies. The progression converges at 23.83 eV, slightly below the position where the band has the highest intensity. This ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathit{u}}^{}{}_{}{}^{}$ state is thus shown to be bound with a dissociation energy ${\mathit{D}}_0$ of 2.5 eV. The assignments are confirmed by a/Iab initio /P calculations, which also provide a vibrational analysis and potential curves that agree very well with the experimental results. These calculations show that the potential curves follow the electron configurations rather than the adiabatic curves in the inner-valence region.

Various momentum-space properties are computed for the Be atom and its isoelectronic sequence from highly accurate configuration-interaction wave functions that include more than 90% of the correlation energy. We assess the effects of electron correlation in momentum space by making a comparison with the results obtained from the Hartree-Fock level. The results reveal differences that indicate that the inclusion of electron correlation is necessary if one is to obtain highly accurate momentum space quantities. Additionally, our results show that the sum of the position and momentum-space entropies increases in going from the Hartree-Fock to the configuration-interaction level, supporting the argument that this sum may be used in assessing the quality of a basis set. The observation that the entropy sum and the other calculated properties remain stable with the inclusion of more electron correlation suggests that these properties are not sensitive to the amount of electron correlation and that density convergence criteria may be more useful in obtaining an accurate electronic distribution than criteria based solely on the amount of correlation energy.

A general analysis of the two-body Dirac equation is presented for the case of equal masses interacting via a static Coulomb potential. Radial equations are derived and their analytical structure is discussed. Standard analytical and perturbative methods have failed to provide solutions to the radial equations due to the presence of the singularity on the negative radial axis at roughly the distance of the classical electron radius. The exact radial equations are solved using finite-element analysis, and the low-lying bound states are obtained to an accuracy of one part in ${10}^{18}$. The effect of the singularity is clearly seen in the structure of the finite-element radial components.

Topographies of ground-state electron-momentum densities (EMD’s), γ(p), are studied for a number of diatomic as well as polyatomic molecules and compared with the corresponding separated atom-momentum densities with a view to bring out clearly the effect of bonding from a momentum-space standpoint. All possible critical points of rank three are seen to occur in the molecular EMD topology. Some linear molecules, in particular, are seen to possess a ring of stable critical points. Diatomic molecules constituted of atoms with exclusively s-type orbitals exhibit, in their γ(p) topography, a maximum at p=0. Whenever for any di- or polyatomic system γ(0) is maximal, it turns out to be a unique critical point, whereas for all other cases of criticality at p=0 a definite hierarchy, dictated solely by the criticality at the origin, in the nature of critical points elsewhere is observed. Criticality at p=0, while being imperative, is seen to have a direct bearing on the anisotropies in EMD that manifestly are chiefly characteristic of molecular, rather than separated-atom, EMD. Further, from studies carried out on some isoelectronic series of diversified polyatomic systems, a correlation between the curvatures associated with the p=0 criticality and distribution polarity is discovered.

The Kohn-Sham energy with exact exchange [using the exact Hartree-Fock (HF) exchange but an approximate correlation-energy functional] may be computed very accurately by adding the correlation obtained from the HF density to the total HF energy. Three density functionals are used: local spin density (LSD), LSD with self-interaction correction, and LSD with generalized gradient correction. This scheme has been extended (Lie-Clementi, Colle-Salvetti, and Moscardo–San-Fabian) to be used with general-valence-bond (GVB) energies and wave functions, so that the extra correlation included in the GVB energy is not counted again. The effect of all these approximate correlations on HF or GVB spectroscopic constants (${\mathit{R}}_{\mathit{e}}$,${\mathrm{\omega }}_{\mathit{e}}$, and ${\mathit{D}}_{\mathit{e}}$) is studied. Approximate relations showing how correlation affects them are derived, and may be summarized as follows: (1) the effect on ${\mathit{R}}_{\mathit{e}}$ and ${\mathrm{\omega }}_{\mathit{e}}$ depends only on the correlation derivative at ${\mathit{R}}_{\mathit{e}}$, and (2) the effect on ${\mathit{D}}_{\mathit{e}}$ depends mainly on the correlation difference between quasidissociated and equilibrium geometries. A consequence is that all the correlation corrections tested here give larger ${\mathrm{\omega }}_{\mathit{e}}$ and ${\mathit{D}}_{\mathit{e}}$ and shorter ${\mathit{R}}_{\mathit{e}}$ than the uncorrected HF or GVB values. This trend is correct for ${\mathit{D}}_{\mathit{e}}$ for both HF and GVB. For ${\mathit{R}}_{\mathit{e}}$ and ${\mathrm{\omega }}_{\mathit{e}}$, it is correct in most cases for GVB, but it often fails for the HF cases. A comparison is made with Kohn-Sham calculations with both exchange and correlation approximated. As a final conclusion, it is found that, within the present scheme, a qualitatively correct HF or GVB potential-energy curve, together with a correlation-energy approximation with correct dissociation behavior, is crucial for obtaining good estimates of spectroscopic constants.

Tung has constructed a sum-rule-constrained classical binary-collision model for the estimation of generalized oscillator strengths (GOS’s) of the 1s and 2s subshells of atoms. He applied three sum rules to determine the momentum-dependent parameters introduced in the GOS function based on the classical binary-collision model. Several deficiencies have then been found regarding these sum rules that adopted the less accurate hydrogenic model and included the unwanted contribution from discrete excitations. In the present work, we have reconstructed this model by employing improved sum rules obtained from Hartree-Fock-Slater matrix element calculations. The refined model has been successfully applied to estimate ionization generalized oscillator strengths of atomic K and L shells.