Rigorous conditions for the existence of bound states at the threshold in the two-particle case

In the framework of non-relativistic quantum mechanics and with the help of the Greens functions formalism we study the behavior of weakly bound states as they approach the continuum threshold. Through estimating the Green's function for positive potentials we derive rigorously the upper bound on the wave function, which helps to control its falloff. In particular, we prove that for potentials whose repulsive part decays slower than $1/r^{2}$ the bound states approaching the threshold do not spread and eventually become bound states at the threshold. This means that such systems never reach supersizes, which would extend far beyond the effective range of attraction. The method presented here is applicable in the many--body case

Time Asymmetric Quantum Physics

Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.Comment: Tex file with 2 figure

The Single-Particle density of States, Bound States, Phase-Shift Flip, and a Resonance in the Presence of an Aharonov-Bohm Potential

Both the nonrelativistic scattering and the spectrum in the presence of the Aharonov-Bohm potential are analyzed. The single-particle density of states (DOS) for different self-adjoint extensions is calculated. The DOS provides a link between different physical quantities and is a natural starting point for their calculation. The consequences of an asymmetry of the S matrix for the generic self-adjoint extension are examined. I. Introduction II. Impenetrable flux tube and the density of states III. Penetrable flux tube and self-adjoint extensions IV. The S matrix and scattering cross sections V. The Krein-Friedel formula and the resonance VI. Regularization VII. The R --> 0 limit and the interpretation of self-adjoint extensions VIII. Energy calculations IX. The Hall effect in the dilute vortex limit X. Persistent current of free electrons in the plane pierced by a flux tube XI. The 2nd virial coefficient of nonrelativistic interacting anyons XII. Discussion of the results and open questionsComment: 68 pages, plain latex, 7 figures, 3 references and one figure added plus a few minor text correction

Doublet and quartet states of Li

Electronic states of the molecular lithium anion are investigated by configuration-interaction calculations. Comparison with the analogously computed potential energy curves for the lowest singlet and triplet states of the neutral Li2 shows that in addition to the well-known stable ground state X$^2\Sigma_u^+$ there also exist metastable excited states of Li$_2^-$. Within the quartet sector, two candidates for such long-lived states are identified and their spectroscopic properties studied

Tricationic metastability by symmetry restrictions: B

To explain the experimentally observed metastability of the trication B23+, we study this system by various ab-initio methods. Whereas the electronic ground state X2Σu+ of B23+ turns out to be unstable, the potential energy curves of the lowest excited state 12Πu and of the quartet state 14Σg− form barriers that support quasi-bound vibronic states. The lifetimes of these states are not only determined by the respective (dissociative) tunnelling rates, but also by possible radiative electronic transitions and predissociation via spin-orbit coupling, where the latter furnish the decisive decay mechanism for the low-lying vibronic levels. In case of the quadruply charged system B24+, our computations do not predict any metastable states in the low-lying electronic spectrum. The deviation from a purely Coulombic repulsive behaviour in B24+ is quantified by fitting the potential energy curves to a modified Murrell-Sorbie function

Information entropy for relativistic angular densities

Entropies for the relavant Figures in the manuscript "Relativistic Angular Densities and their Information Entropy

Data for: A theoretical study of the dication P22+_2^{2+}

Results of MRCI computations on electronic states of the dicationic diphoshoro

Information entropy for relativistic angular densities

Entropies for the relavant Figures in the manuscript "Relativistic Angular Densities and their Information Entropy