Wave packets in quantum theory of collisions

Two methodological troubles of the quantum theory of collisions are considered. The first is the undesirable interference of the incident and scattered waves in the stationary approach to scattering. The second concerns the nonstationary approach to the theory of collisions of the type $a+b\to c+d$. In order to calculate the cross section one uses the matrix element $$ of the $S$-matrix. The element is proportional to $\delta$-function expressing the energy conservation. The corresponding probability $|< cd|S|ab>|^2$ contains $\delta^2$ which is mathematically senseless. The known regular way to overcome the difficulty seems to be unsatisfactory. In this paper, both the troubles are resolved using wave packets of incident particles.Comment: 14 page

Moving system with speeded-up evolution

In the classical (non-quantum) relativity theory the course of the moving clock is dilated as compared to the course of the clock at rest (the Einstein dilation). Any unstable system may be regarded as a clock. The time evolution (e.g., the decay) of a uniformly moving physical system is considered using the relativistic quantum theory. The example of a moving system is given whose evolution turns out to be speeded-up instead of being dilated. A discussion of this paradoxical result is presented.Comment: 10 pages, LaTe

New solutions of relativistic wave equations in magnetic fields and longitudinal fields

We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation, which reduces effectively the number of variables in the initial equations. Then we use the corresponding representations to construct new sets of exact solutions, which may have a physical interest. Namely, we present new sets of stationary and nonstationary solutions in magnetic field and in some superpositions of electric and magnetic fields.Comment: 25 pages, LaTex fil

Phenomenological theory of phase transitions in epitaxial BaxSr(1-x)TiO3 thin films

A phenomenological thermodynamic theory of BaxSr(1-x)TiO3 (BST-x) thin films epitaxially grown on cubic substrates is developed using the Landau-Devonshire approach. The eighth-order thermodynamic potential for BT single crystal and modified fourth-order potential for ST single crystal were used as starting potentials for the end-members of the solid solution with the aim to develop potential of BST-$x$ solid solution valid at high temperatures. Several coefficients of these potentials for BT were changed to obtain reasonable agreement between theory and experimental phase diagram for BST-x (x > 0.2) solid solutions. For low Ba content we constructed the specific phase diagram where five phases converge at the multiphase point (T_N2 = 47 K, x = 0.028) and all transitions are of the second order. The "concentration-misfit strain" phase diagrams for BST-x thin films at room temperature and "temperature-misfit strain" phase diagrams for particular concentrations are constructed and discussed. Near T_N2 coupling between polarization and structural order parameter in the epitaxial film is modified considerably and large number of new phases not present in the bulk materials appear on the phase diagram.Comment: 8 pages 5 figure