Pseudowave Functions Research Articles

Analytic properties of pseudo-potentials

A new examination of the theory of pseudo-potentials, necessitated by the discovery that smoothness of the pseudo-wave function is not a relevant criterion for their effectiveness, provides an understanding of the analytic properties of pseudo-potentials in terms of their pseudo-core energies Ecprime. In particular, it is found for Hermitian pseudo-potentials that, if Ecprime greater, similar <c|H0|c>, the Born series cannot have good convergence properties, but, for Ecprime = 0, the series has good asymptotic convergence. The new pseudo-potential, with Ecprime = 0, is the correct form to use at all energies, but differs substantially from other forms only at higher energies. Its effectiveness is demonstrated by a model calculation.

On pseudo wave functions

The pseudo wave function in the Cohen-Heine scheme is expressed in terms of the complete orthonormal set of the wave functions of the original Hamiltonian and the expansion coefficients are calculated. The applicability of this scheme is discussed.

Propagation of Electromagnetic Waves in a Nonuniformly Ionized Medium

This paper is concerned with the theoretical solution of electromagnetic wave propagation through a nonuniform plasma sheath bounded by a plane infinite conductor. The governing differential equation yields a set of pseudo wave functions upon which all subsequent analysis is based. An exact solution is obtained for normal incidence and an excellent approximate solution for oblique incidence in the particular case of an assumed exponentially varying conductivity distribution. The procedures developed are applied to two practical cases, namely a penetration problem and a radiation problem. After establishing the proper orders of magnitude of the involved parameters from practical considerations, appropriate numerical data are obtained.