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A random potential approach to the non-relativistic and relativistic N-particle problem

Klaus Dietz

Published Jan 1, 1981• 0 citations
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arXiv:1511.07901•Nov 24, 2015•5 citations

Probability in relativistic particle theory

Patrick Suppes

Erkenntnis•Jul 1, 1981•3 citations
A traversal time that has no problem of superluminality was advanced for particles to tunnel through potential barriers in the non-relativistic quantum theory in a previous paper by C.-F. Li and Q. Wang, Physica B 296 (2001) 356. This time is generalized in this paper to Dirac's relativistic quantum theory. Both evanescent and propagating cases are considered. It is shown that the traversal time in the evanescent case has much the same properties as in the non-relativistic quantum theory and thus has no problem of superluminality. It also gets rid of the problem of superluminality in the propagating case. Comparisons with the dwell time, the group delay, and the velocity of monochromatic front are also made.
We show that the first order form of the Schrodinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local gauge invariance. In addition, we study the problem of a spin up particle incident on a finite potential barrier and show that the known quantum mechanical results are obtained. Finally, we consider the symmetric potential well and show that the quantum mechanical expression for the quantized energy levels of a particle is obtained with periodic boundary conditions. Based on these conclusions, we propose that the equation introduced in [1] is the non-relativistic limit of the Dirac equation and more appropriately describes spin 1/2 particles in the non-relativistic limit.