The discrete spectrum for a Morse oscillator is found using an SO(2, 1) algebra. Since this algebra does not prove to be appropriate compute matrix elements the eigenfunctions, author construct B1-type with aid of auxiliary angle variable. Matrix and recurrence relations are several useful operators limit in which anharmonicity tends zero studied.

Whereas the determinantal wave functions constructed from solutions of Hartree-Fock equations satisfy virial theorem, those self-consistent-field schemes with a local exchange approximation do not necessarily. A scaling procedure, which goes back to Fock, allows considerable improvement and good agreement results. The theorem criterion agrees previous empirically based assertions that Slater's potential "overestimates" effects. In addition, also in an ab initio way, it can be added Kohn...

An ab anitio SCF–LCAO–MO study of nonadditive three- and four-body interaction energies in Mg3 (equilateral linear) Mg4 (tetrahedral) clusters is presented. The relative importance these few-body terms to the energy at most 39% for 8% terms. This lies marked contrast with case Be where can have a weight up 76%, 31.6%, respectively. reason such radically different effects discussed. Some new results Be3, Be4, Be5 are presented confirming this multibody expansions expected be very slowly...

Investigation is made of the symmetry and degeneracy Dirac equation for a Coulomb potential with fixed center bearing both electric magnetic charge. Seen from viewpoint classical mechanics, relativistic precession removes accidental nonrelativistic potential, may be so severe as to lead spiral rather than precessing elliptic orbits. The restored by introduction vector which combats leads closed An angular momentum Runge are found ``symmetric'' arbitrary values nuclear charges. A related...

We study the quantum dynamics of a nonrelativistic neutral particle with spin in inhomogeneous external magnetic fields. first consider fields one-dimensional inhomogeneities, both unphysical and physical, construct corresponding analytic propagators. then two-dimensional inhomogeneities develop an appropriate numerical propagation method. propagate initial states exhibiting different degrees space localization various configurations, including pure mixed states. evolution their densities...

We assess several widely used vector models of a Gaussian laser beam in the context more accurate diffraction integration. For analysis, we present streamlined derivation fields uniformly polarized reflected from an ideal parabolic mirror, both inside and outside resulting focus. This exact solution to Maxwell's equations, first developed 1920 by V. S. Ignatovsky, is highly relevant high-intensity experiments since boundary conditions at focusing optic dictate form focus manner analogous...

Abstract The algebra of the two‐dimensional harmonic oscillator is exploited to obtain matrix elements between eigenstates Morse potential. This follows after mapping latter into radial equation former problem by means a change variable and use angular as dummy variable.

We formulate the problem of finding narrow positive energy resonances in a deep potential well as an eigenvalue (thereby extending scope discrete spectrum problem). determine number exactly soluble case. The method is then applied to nonperturbative treatment magnetic occurring charge-dipole interactions, and existence previously conjectured high mass this model proved.

A variational principle is presented for the ground state energy in terms of one-particle density matrix. The functional expression matrix obtained as limit zero temperature free energy. This achieved by adding a nonlocal external potential to N-body Hamiltonian and obtaining renormalized equation instead Green's function. By eliminating source it was possible express

This study was a part of the second antibody modeling assessment. The assessment is blind performance multiple software programs used for homology modeling. In study, research groups were given sequences 11 antibodies and asked to predict their corresponding structures. results measured using root-mean-square deviation (rmsd) between submitted models X-ray crystal 10 cases, SmrtMolAntibody show good agreement first stage, average rmsd 1.4 Å. Average values framework 1.2 Å H3 loop 3.0 stage...

We study the temporal evolution of a coherent state under action parametric oscillator and nonlinear Kerr-like medium. make use interaction picture representation an exact time operator for independent part Hamiltonian. approximate Hamiltonian in such way as to it member Lie algebra. The corresponding behaves like squeezing due dependence oscillator's frequency. analyze probability amplitude auto correlation function different parameters we find very good agreement between our results...

An alternative form of building up the terms associated 'modified Aufbau procedure' requires less ad hoc assumptions states elements periodic table is established. This modified than (n+l,n) recipe. It furthermore allows one to relate atomic magic numbers degeneracies irreducible representations (IR) a group built as direct product three SU(2) groups, making for better theoretical understanding periodicity elements.

The idea of emergence originates from the fact that global effects emerge local interactions producing a collective coherent behavior. A particular instance is illustrated by flocking model interacting “boids” encompassing two antagonistic conducts—consensus and frustration—giving rise to highly complex, unpredictable, cohesive motion arising consensus can be described in terms three ordered dynamic phases. Once frustration included model, phases for specific groups flockmates, transitions...

Abstract Solid‐state calculations were performed with the program CASTEP to analyze some electronic structure features of crystal compound Li 6 Gd(BO 3 ) (LIGDBO), which is known be an efficient gamma radiation detector, in particular when doped rare‐earth ions. The this material displays a clear 1‐D preference, where chains atoms are formed along one crystalline axes. These quasilinear responsible for energy transfer occurring system prior actual detection. To elucidate on aspects former...

Abstract The explicit form of a projection operator constructed from linearly dependent set is found. relationships with canonical orthonormalization and the cofactor matrix set's metric are discussed. Similar expressions obtained for inner positive definite using set.

Many questions concerning the theoretical understanding of table elements still remain open. In particular existence atomic magic numbers associated with noble gas behaviour has led to a search for approximate hidden symmetries. Such symmetry is obtained here without any postulates. Instead, authors follow Fock's analysis hydrogen atom who projected it on 4-dimensional hypersphere. this case corresponding mapped system quantal top in 4-dimensions. The top's group G provides representations...

A unified and completely time-independent approach based on Feshbach's formalism for nuclear reactions, in which radiative nonradiative processes are treated an equal basis, is used to describe the behavior of isolated molecules a radiation field. The expressions developed complete link excited states measurable lifetime resonances arising from action Green functions. Approximations form assumption that ground can be described as Born–Oppenheimer finally introduced only show how matrix...

We derive an expression for the exchange energy integral in terms of density case light atoms containing s and p electrons. start from approximate functional form matrix electron cloud presence attractive nucleus. An important restriction to consider is Pauli principle. A correction factor included account multipole expansion average way. The results we obtain, both closed open shells, are within a few percent exact integral.