Question

In class we considered quantum tunneling of a particle of energy Eo through a barrier of potential Vofor Vo > Eo. Here we focus on two aspects of the problem we ignored in class. In order to simplify we will only consider the initial first half of the barrier as shown below RegionI xS0 Regionx 20 Il There are two cases to consider: Eo< Vo Considered in class E>Vo Not considered in class Here we will focus on the second case, where E。> Classically the particle would simply not know the barrier is there and continue on its way to positive values of x (although with a reduced velocity). However, for quantum particles this is not the case as you will show a) Consider a particle of mass, m, and energy Eo>V approaching the barrier from-x space in region I. Write the wave functions for regions I and II assuming reflection can occur. Let k, and k2 be the wave vectors in region I and II, A be the amplitude of the incident wave in region I B be the amplitude of the reflected wave and C the amplitude in the transmitted wave (ie. for particles moving in the +x direction in region II) b) Apply the boundary conditions at x-0 using the postulates given earlier in class (and in the book) and obtain two equations relatingA, B, C,ki.k2

Answer 1