Abstract Symmetry considerations are taken into account when a particle in square well potential is studied. This system may display natural degeneracy, accidental degeneracy or systematic depending on the depth of potential. In order to obtain solutions associated with an arbitrary algebraic discrete variable representation approach based Pöschl-Teller functions proposed. It proved that geomet...

1 9. Conclusions Bibliography Glossary Bohr hypotheses: Set of hypotheses that Bohr introduced to explain the stability of the atom. Coulomb potential: Potential that holds the electrons attached to the nucleus. Creation and Annihilation operators: Mathematical objects that create or annihilate particles. Dynamical phase: It is the factor that contains the time dependence of the wave function. ...

One of the main criticisms to game theory concerns the assumption of full rationality. Logit dynamics is a decentralized algorithm in which a level of irrationality (a.k.a. “noise”) is introduced in players’ behavior. In this context, the solution concept of interest becomes the logit equilibrium, as opposed to Nash equilibria. Logit equilibria are distributions over strategy profiles that poss...

Noise-induced jumping between metastable states in a potential depends on the structure of the noise. For an alpha-stable noise, jumping triggered by single extreme events contributes to the transition probability. This is also called Levy flights and might be of importance in triggering sudden changes in geophysical flow and perhaps even climatic changes. The steady-state statistics is also in...

The assessment of model fit is a more complex and indeterminate process than is commonly acknowledged by researchers who use structural equation modeling (SEM) techniques. Even models that are well fitting according to commonly used statistical tests and descriptive fit indices can have significant problems and ambiguities. The authors discuss 7 potential difficulties that can arise and that sh...

We consider the local and global well-posedness of the coupled nonlinear wave equations u tt − ∆u + g 1 (u t) = f 1 (u, v) v tt − ∆v + g 2 (v t) = f 2 (u, v), in a bounded domain Ω ⊂ R n with a nonlinear Robin boundary condition on u and a zero boundary conditions on v. The nonlinearities f 1 (u, v) and f 2 (u, v) are with supercritical exponents representing strong sources, while g 1 (u t) and...