Stationary Solutions of the Klein-Gordon Equation in a Potential Field

arXiv1008.4224MaRDI QIDQ6220369

Author name not available (Why is that?)

Publication date: 25 August 2010

Abstract: We seek to introduce a mathematical method to derive the Klein-Gordon equation and a set of relevant laws strictly, which combines the relativistic wave functions in two inertial frames of reference. If we define the stationary state wave functions as special solutions like $Psi(mathbfr,t)=psi(mathbfr)e^{-iEt/hbar}$, and define $m=E/c^2$, which is called the mass of the system, then the Klein-Gordon equation can clearly be expressed in a better form when compared with the non-relativistic limit, which not only allows us to transplant the solving approach of the Schr"{o}dinger equation into the relativistic wave equations, but also proves that the stationary solutions of the Klein-Gordon equation in a potential field have the probability significance. For comparison, we have also discussed the Dirac equation. By introducing the concept of system mass into the Klein-Gordon equation with the scalar and vector potentials, we prove that if the Schr"{o dinger equation in a certain potential field can be solved exactly, then under the condition that the scalar and vector potentials are equal, the Klein-Gordon equation in the same potential field can also be solved exactly by using the same method.

This page was built for publication: Stationary Solutions of the Klein-Gordon Equation in a Potential Field

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6220369)