Scattering of a Klein–Gordon particle by a smooth barrier

Abstract

We present the study of the one-dimensional Klein-Gordon equation by a smooth barrier. The scattering solutions are given in terms of the Whittaker M κ,µ (x) function. The reflection and transmission coefficients are calculated in terms of the energy, the height and the smoothness of the potential barrier. For any value of the smoothness parameter we observed transmission resonances.

Bound states of a Klein-Gordon particle in presence of a smooth potential well

“…The analytical solution of the one-dimensional time-independent Klein-Gordon equation for different potentials has been caused of a lot of interest in recent years, for both bound states 4-10 and scattering solutions. 6,8,[10][11][12][13][14][15][16][17][18][19][20] It has allowed the understanding of several physical phenomena of Relativistic Quantum Mechanics such as the antiparticle bound state, 2,21 transmission resonances, [11][12][13] and superradiance. 14,[22][23][24] The article is structured as follows: Sec.…”