Piotr Rozmej

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This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a(More)
An alternative way for the derivation of the new Korteweg-de Vries (KdV)-type equation is presented. The equation contains terms depending on the bottom topography (there are six new terms in all, three of which are caused by the unevenness of the bottom). It is obtained in the second-order perturbative approach in the weakly nonlinear, dispersive, and long(More)
In the paper we study some numerical solutions to Volterra equations which interpolate heat and wave equations. We present a scheme for construction of approximate numerical solutions for one and two spatial dimensions. Some solutions to the stochastic version of such equations (for one spatial dimension) are presented as well. ∗ Extended version of the(More)
We remind the properties of the intelligent (and quasi-intelligent) spin states introduced by Aragone et al. We use these states to construct families of coherent wave packets on the sphere and we sketch the time evolution of these wave packets for a rigid body molecule. PACS numbers: 03.65.Sq Submitted to: Institute of Physics Publishing The eigenstates of(More)
The aim of this paper is to give an overview of theoretical predictions on heights of fission barriers for superheavy nuclei. The macroscopic-microscopic model of the potential energy as a function of nuclear shape is briefly presented. Immersion method of searching for saddle points determining the barrier heights which has been recently adapted to nuclear(More)
We discuss an extension of the theory of spin-orbit pendulum phenomenon given in [1] to relativistic approach. It is done within the so called Dirac Oscillator. Our first results, focusing on circular wave packet motion have been published recently [2]. The scope of this paper is motion of a linear wave packet. In relativistic approach we found(More)
Time evolution of radial wave packets built from the eigenstates of Dirac equation for a hydrogenic systems is considered. Radial wave packets are constructed from the states of different n quantum number and the same lowest angular momentum. In general they exhibit a kind of breathing motion with dispersion and (partial) revivals. Calculations show that(More)
This article discusses the properties of time evolution of wave packets in a few systems. Dynamics of wave packet motion for Rydberg atoms with the hierarchy of collapses and revivals is briefly reviewed. The main part of the paper focuses on the new mechanism of quantum recurrences in wave packet dynamics. This mechanism can occur in any physical system(More)
In [1] we have introduced a collective model which allows to study the bulk and surface modes of a nuclear droplet as function of its density and temperature T . The description is based on the diabatic approach to dissipative collective motion and – in the local density approximation – yields equations of motion for small amplitudes, where the mass and(More)