A novel interpretation of the Klein-Gordon equation

Details A novel interpretation of the Klein-Gordon equation A novel interpretation of the Klein-Gordon equation

2007-06-27

arxiv.org/abs/0706.4075v3

Found. Phys. v40; 313-332, 2010.

Physics

Quantum Physics

v3: Extensively revised version accepted for publication by Found. Phys

Scientific paper

10.1007/s10701-009-9398-2

The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrodinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an initial boundary condition, this paper considers the possibility that the solutions are determined by both an initial and a final boundary condition. By constructing an invariant joint probability distribution from the size of the solution space, it is shown that the usual measurement probabilities can nearly be recovered in the non-relativistic limit, provided that neither boundary constrains the energy to a precision near hbar/T (where T is the time duration between the boundary conditions). Otherwise, deviations from standard quantum mechanics are predicted.

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