Quantum Field Theory Lecture 2: Klein Paradox (Transmission/Reflection from Potential Barrier)

welcome to the second lecture in Quantum field Theory now this time we will begin discussing decline Paradox decline Paradox is very very interesting because it will show us some further problems with the client-golden equation but also give us some interesting hints as to where this entire thing is going so what we will do here is we will consider this situation we have some particle that is incident on this barrier okay so there is no potential here and then there is an electrostatic potential okay so it's not just any potential it is an electrostatic potential in this region 2 which starts at Z equals zero so let's study the situation let's find the transmission coefficient the reflection coefficient and you know the way we have done it in the past so to do that um we will Begin by writing down our equation okay so we know that we have the Klein Gordon equation M squared acting on our wave function now this is going to be a function of Z and a end of time actually equal to zero and of course let's keep in mind that the dalam version here this square is called the Italian version this is simply D mu D mu okay so what we now want to do is keep in mind that now we're going to be dealing with an electrostatic potential which means of course that we need to take into account what we have learned in courses in electromagnetic Theory and in particular we need to take into account that when we are in the presence of this electric field what we will have is that our derivative here right because of the change in in this situation where we have this new potential we'll go to the MU plus i e a meal right and similarly the MU covariant will go to the MU plus I E AMU okay this is called minimal coupling um so if you have not seen before I before we will go a little bit more into it