Question

A electric beam is incident on a potential barrier at height 0.03ev and of infinite with find the reflection coefficient of the barrier if the energy of the incident electric beam be (a)0.04ev(b)0.025ev(c)0.03ev.

Answer 1

(i)The transmission coefficient for the step-like potential 

$$T=\frac{4\sqrt{E}\sqrt{E-V_0}}{(\sqrt{E}+\sqrt{E-V_0})^2}$$ $$=\frac{4\sqrt{0.04}\sqrt{0.04-0.03}}{(\sqrt{0.04}+\sqrt{0.04-0.03})^2}=0.889$$

The reflection coefficient

$$R=1-T=1-0.889=0.111$$

(ii) The transition does not occur since $E<V_o$

(iii) The transmission coefficient for the step-like potential 

$$T=\frac{4\sqrt{E}\sqrt{E-V_0}}{(\sqrt{E}+\sqrt{E-V_0})^2}$$ $$=\frac{4\sqrt{0.03}\sqrt{0.03-0.03}}{(\sqrt{0.03}+\sqrt{0.03-0.03})^2}=0$$

The reflection coefficient

$$R=1-T=1-0=1$$