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Link Between the One Dimensional Dirac Equations and Two Velocities in Nonrelativistic Quantum Mechanics?
2019
Zenodo
The Dirac equation is often obtained through linearization of the Klein-Gordon equation. This leads to a 2x2 matrix system for one dimension, thus two functions u(x) and v(x) from the two- vector appear naturally. The Schrodinger equation may then be obtained through the nonrelativistic limit, as has shown in the literature. In this note, we consider the idea of two velocities in nonrelativistic quantum mechanics, namely 1/m d/dx W / W and (1/m) sqrt[ - d/dx d/dx W(x)/W(x)] where W(x) is the
doi:10.5281/zenodo.3376305
fatcat:6n7qdkl35rgmvpy7obu2f2ywra