Computational derivation of quantum relativist electromagnetic systems with forward-backward space-time shifts

Dubois, Daniel M.
May 2000
AIP Conference Proceedings;2000, Vol. 517 Issue 1, p417
Academic Journal
This paper is a continuation of our preceding paper dealing with computational derivation of the Klein–Gordon quantum relativist equation and the Schro¨dinger quantum equation with forward and backward space-time shifts. The first part introduces forward and backward derivatives for discrete and continuous systems. Generalized complex discrete and continuous derivatives are deduced. The second part deduces the Klein–Gordon equation from the space-time complex continuous derivatives. These derivatives take into account forward-backward space-time shifts related to an internal phase velocity u. The internal group velocity v is related to the speed of light u.v=c[sup 2] and to the external group and phase velocities u.v=v[sub g].v[sub p]. Without time shift, the Schro¨dinger equation is deduced, with a supplementary term, which could represent a reference potential. The third part deduces the Quantum Relativist Klein–Gordon equation for a particle in an electromagnetic field. © 2000 American Institute of Physics.


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