Klein's paradox and quantum Hamiltonian dynamics in complex spacetime

Abstract

In this paper, along with previous investigation in Payandeh et al., Chin. Phys. C 37, 113103 (2013), we will use the full set of free Dirac's solutions to remove the Klein's paradox. However, we choose a different approach, namely the relativistic quantum Hamilton–Jacobi equations and the resultant quantum states. We show that this full set of solutions can also be retained as a single wave function, and also possess the potential of removing Klein's paradox.