Chapter 7, Problem 1Q

To determine

The way in which amplitude of the reflected wave and incident wave changes as the barrier height is reduced.

Answer to Problem 1Q

As the barrier height is reduced amplitude of transmitted wave increases while amplitude of incident wave reduces.

Explanation of Solution

Write the expression for relation between transmission probability and reflection probability.

     $T\left(E\right)+R\left(E\right)=1$

Here, $T\left(E\right)$ is the transmission probability and $R\left(E\right)$ is the reflection probability.

When barrier height is reduced and potential energy is greater than particle energy then transmission probability will increase and from the above expression it can be concluded that reflection probability will decrease.

Conclusion:

Thus, as the barrier height is reduced amplitude of transmitted wave increased while amplitude of incident wave reduced.