A 2-D computer simulation of a coaxial plasma device depending on the conservation equations of electrons, ions and excited atoms together with the Poisson equation for a plasma gun is carried out. Some characteristics of the plasma focus device (PF) such as critical wave numbers a c and voltages U c in the cases of various pressures Pare estimated in order to satisfy the necessary conditions of traveling particle densities (i.e. plasma patterns) via a linear analysis. Oscillatory solutions are characterized by a nonzero imaginary part of the growth rate $$ \Im $$(σ) for all cases. The model also predicts the minimal voltage ranges of the system for certain pressure intervals.
In this paper, using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Klein-Gordon equation with the vector and scalar Hulthén potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of t-waves scattering states are presented. The normalized wave functions expressed in terms of hypergeometric functions of scattering states on the “k/2π scale” and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solution is discussed.
The Green function for a Dirac particle subject to a plane wave field is constructed according to the path integral approach and the Barut’s electron model. Then it is exactly determined after having fixed a matrix U chosen so that the equations of motion are those of a free particle, and by using the properties of the plane wave and also with some shifts.
We study the application of the asymptotic iteration method to the Khare-Mandal potential and its PT-symmetric partner. The eigenvalues and eigenfunctions for both potentials are obtained analytically. We have shown that although the quasi-exactly solvable energy eigenvalues of the Khare-Mandal potential are found to be in complex conjugate pairs for certain values of potential parameters, its PT-symmetric partner exhibits real energy eigenvalues in all cases.
The one-dimensional path decomposition expression for the step potential and mass is formulated. The propagator is analytically determined and the limiting case m 1; m 2 → m is exactly obtained.
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