TL;DR
This paper solves the one-dimensional Feshbach-Villars equation for a spin-1/2 particle in a scalar potential, deriving wave functions and analyzing boundary conditions to predict pair creation phenomena.
Contribution
It provides explicit solutions for the Feshbach-Villars equation with a scalar potential and tests boundary conditions related to pair creation.
Findings
Wave functions expressed via hypergeometric functions.
Boundary conditions validated for scalar potential step.
Prediction of pair creation from charge density boundary conditions.
Abstract
We solve the one dimensional Feshbach-Villars equation for spin-1/2 particle subjected to a scalar smooth potential. The eight component wave function is given in terms of the hypergeometric functions and via a limiting procedure, the wave functions of the step potential are deduced. These wave functions are used to test the validity of the boundary conditions deduced from the Feshbach-Villars transformation. The creation of pairs is predicted from the boundary condition of the charge density.
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