We used Wick’s normal-ordering technique, squeezed creation and annihilation operators, and a variation method, to find the eigenvalues of the general pure ?x2m potential. Numerical results for low-lying energy levels of pure quadratic, quartic, sextic, octic and decatic potentials, for different values of ? were obtained. Some interesting features of these energy levels are explained.

We consider diffusion-limited reactions A(i)+A(j)--> (1< or =i2 and d> or =2, we argue that the asymptotic density decay for such mutual annihilation processes with equal rates and initial densities is the same as for single-species pair annihilation A+A-->. In d=1, however, particle segregation occurs for all q< infinity. The total density decays accordi...

using positron annihilation spectroscopy M. Liu, R. S. Vallery, D. W. Gidley, M. E. Launey, and J. J. Kruzic Department of Physics, Randall Laboratory, University of Michigan, Ann Arbor, Michigan 48109, USA Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Materials Science, School of Mechanical, Industrial, and Manufacturing Engineering, Oregon...

Eigenstates of the linear combinations a 2 + βa †2 and ab + βa † b † of two boson creation and annihilation operators are presented. The algebraic procedure given here is based on the work of Shanta et al. 1994] for constructing eigenstates of generalized annihilation operators. Expressions for the overlaps of these states with the number states, the coherent states and the squeezed states are ...

We compute the next-to-next-to-leading order (NNLO) QCD corrections to the six most important event shape variables related to three-particle final states in electronpositron annihilation. The corrections are sizeable for all variables, however their magnitude is substantially different for different observables. We observe that the NNLO corrections yield a considerably better agreement between...

Covering-based rough sets are important generalizations of the classical rough sets of Pawlak. A common way to shape lower and upper approximations within this framework is by means of a neighborhood operator. In this article, we study 24 such neighborhood operators that can be derived from a single covering. We verify equalities between them, reducing the original collection to 13 different ne...

It is argued that in the antiproton-proton annihilation into two mesons p̄p −→ m1m2, the origin of different angular momentum selection rules commonly obtained for planar annihilation diagrams A2 and for non-planar rearrangement diagrams R2 lies in the omission of momentum transfer between an annihilated antiquark-quark pair and a remaining quark or antiquark. Therefore, there is no reason for d...