Hello! I want to prove that the probability current is a continuous entity at the boundaries of the square for the situation of 0< E< Vo in the problem where V is zero except a finite region in space where it is +Vo and we consider an incoming particle from the left(for example). I thought that in the region of the non-zero potential we have an evanescent wave(described by real exponentials), so the probability current there is zero because there is no time change for the probability of finding the particle inside the region of non zero potential energy and thus the continuity equation gives us that the current there must be zero. But this is clearly wrong because: If the current there is zero then the current in every region would be zero since each current is independent of time and space, which means total reflection and no tunneling in the more general case. Otherwise the current would not be continuous. Clearly, i am getting something wrong! Please, help me..Thank you!