Solution of the Dirac Equation for a Dirac Particle in a Yukawa Field

Abstract

The solution of the Dirac equation for a massive spin ½ particle in a Yukawa-type potential is investigated by transforming the radial form of the Dirac equation into the Whittaker equation from which we have obtained the desired solutions for the regions near the boundaries of the upper and lower energy continuum, E ≈ ∓ m. Comparison is made with earlier studies.

Analytical computation of amplification of coupling in relativistic equations with Yukawa potential

“…[9] by mistake. Now let us show, that at k close to k min ¼ 0 the two coupled first order differential equations (58) are equivalent to the Schrödinger equation (11).…”

“…The coupling constant k of the Yukawa potential (2) is not explicitly contained in Eq. (11). The question can arise as to where did k disappear.…”

“…The Dirac equation in the presence of spherical potential VðrÞ reduces to the two coupled first order ordinary differential equations [9,11]: ½E R À mc 2 À VðrÞ f ðrÞ ¼ À hc g 0 ðrÞ þ 1 À k r gðrÞ…”

“…The Dirac equation and the Klein-Gordon equation are the most frequently used wave equations for the descriptions of particle dynamics in relativistic quantum mechanics. In nuclear and high energy physics, as well as in other areas an increasing interest in these equations has appeared in the last decade [1][2][3][4][5][6][7][8][9][10][11].…”

“…Relativistic equations with this widespread potential were solved only for some special cases or only for the energy eigenvalues in the outcome (see, e.g., [9][10][11]17]). The authors of Ref.…”