Volume 18: Pages 95-102, 2005
Relativistic Quantum Mechanics Based on the Equation of Motion md2r/dt2 = F(1 − (v/c)2)
Department of Physics, Soochow University, Shih‐Lin, Taipei, Taiwan
A theory of relativistic quantum mechanics is formulated based on the equation of motion md2r/dt2 = F(1 − (v/c)2). The relativistic quantum mechanics obtained herein maintains the statistical single‐particle interpretation of quantum theory and satisfies Ehrenfest's theorem. This relativistic quantum mechanics contains nonrelativistic quantum mechanics as a low‐speed limit; in contrast, the conventional relativistic quantum mechanics does not. Moreover, this relativistic quantum mechanics does not have those difficulties encountered in the conventional relativistic quantum mechanics, such as negative probability density, Zitterbewegung, Klein paradox, and anomalous phenomena of bound states of a deep potential well.
Keywords: quantum mechanics, relativistic quantum theory, Klein paradox, Zitterbewegung, relativistic quantum field theory, Klein‐Gordon theory, Dirac theory, special relativity, other theories of relativity
Received: August 4, 2004; Published online: December 15, 2008