For the first spinor components of particle and antiparticle states, it is always negative while for the second spinor components of particle and antiparticle states, it is always positive, whatever the height and width of the barrier. These results derive from studying the tunneling time in terms of phase time. Conversely, the second spinor components of particle and antiparticle states may be either subluminal or superluminal depending on the barrier width. For first spinor components of particle and antiparticle states, the tunneling is always superluminal regardless the barrier width. ![]() If the energy difference between the barrier and the particle is positive, and the barrier width is large enough, there is proof that the tunneling may be superluminal. This paper investigates the problem of a relativistic Dirac half-integer spin free particle tunneling through a rectangular quantum-mechanical barrier.
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