# Potential barrier, reflection coefficient

1. Feb 8, 2016

### Incand

1. The problem statement, all variables and given/known data
Electrons are pushed into a grounded metal tube A by the kinetic energy of 100 eV. After having gone through the tube it passes into another tube, B, at some distance from A. Tube B is kept at a potential of -50V. Calculate how many of the electrons are reflected back into the tube A. ( Assume the potential barrier is discontinuous)

2. Relevant equations
If $E>V_0$ for our barrier then we have the wave numbers
$k_1 = \sqrt{\frac{2mE}{\hbar^2}}$ for $x<0$ and
$k_2 = \sqrt{\frac{2m[E-V_0]}{\hbar^2}}$
for the wave functions
$\Psi_1 = Ae^{ik_1x}+Be^{-ik_1x}$ for $x < 0$ and
$\Psi_2 = Ce^{ik_2x}$ for $x>0$.

The reflection coefficient is then
$R = \left(\frac{k_1-k_2}{k_1+k_2}\right)^2$.

3. The attempt at a solution
I have an electric potential difference of $50V$, somehow I need to convert this into an potential energy but I have no idea how to do that so I don't even know if $E>V_0$ or not and the above formulas are applicable.

Assuming they are I can simply $R$ as
$R = \left( \frac{\sqrt{E}-\sqrt{E-V_0}}{\sqrt{E}-V_0} \right)^2$.
Now I don't know $V_0$ but let's guess $V_0 = 50eV$ (seeing the number 50 in the question!) then
$R=\left( \frac{\sqrt{100}-\sqrt{50}}{\sqrt{100}+\sqrt{50}} \right)^2\approx 0.3$
which agrees with the answer to the exercise but I have no idea if $V_0 = 50eV$ or why that is.

2. Feb 9, 2016

### BvU

Potential energy is $qV$ !

3. Feb 9, 2016

### Incand

Thanks, I suspected that but wasn't sure!