Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

Al-Hashimi, Munir; Shalaby, A. M. (2015). Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization. Physical review. D - particles, fields, gravitation, and cosmology, 92(2) American Physical Society 10.1103/PhysRevD.92.025043

Text PhysRevD.92.025043.pdf - Published Version Restricted to registered users only Available under License Publisher holds Copyright. Download (693kB)

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.

Interest & Impact

Downloads

8 since deposited on 11 Sep 2015
0 in the past 12 months

Citations

5 Citations in Web of Science ®
6 Citations in Scopus

Search

in Google Scholar™

Services

Actions (login required)

Edit item

Actions (login required)

Edit item