Chapter 7, Problem 2P

(a)

To determine

The solution of the Schrodinger equation to the left of the step in the range $x<0$, to the right of the step in the range $x>0$.

(b)

To determine

 The expression for reflection coefficient in this case and prove that it can be written in this form: $R=\frac{{\left(k_1-k_2\right)}^2}{{\left(k_1+k_2\right)}^2}$ . The expression for transmission factor using the sum rule obeyed by these coefficients.

(c)

To determine

The value of $R$ and $T$ in the limiting cases of $E\to U$ and $E\to \infty$ .