Case of Delta-Function Barrier

Let us consider the case of a delta-function barrier V(x) = A.5(jc)(A. 0). The Schrodinger equation to be solved is 

Since the plane waves exp( jLjc) with k = are the independent solutions 

One more condition is obtained by integrating the Schrodinger equation over the interval (—e, e) as 

Considering the case that the incident wave comes in from the left side, we have Ar = 1 and 5/ = 0. Putting A = r (reflection amplitude) and fir = t (transmission amplitude) and solving Equations (2.3) and (2.5), we have 

---