Is E<mc^2 Critical for the Klein Paradox in Potential Step Analysis?

[Joker93]

Hello!
I am trying to work out the various cases for the potential step problem in the context of the Klein Gordon equation.

I was wondering if one must consider the situation where E<mc^2 when working out the situation of
E-mc^2 <V< E+mc^2 where V is the value of the potential after the step.

Thanks!

 

[azntoon]

Yes, it is important to consider the situation where E<mc^2 when working out the potential step problem in the context of the Klein Gordon equation. This is because if E<mc^2, then the particle will not be able to tunnel through the potential barrier. In this case, the wave function must be reflected and not transmitted.