4. (5 pts) Consider a potential barrier
$U(x) = 0$ for $x < 0$
$= U_0$ for $0 \le x \le L$
$= 0$ for $x > L$.
For an electron with energy $E > U_0$, calculate the wavelength of the wavefunction in all three
regions $x < 0$, $0 \le x \le L$, and $L < x$. Sketch the wavefunction, make sure it reflects the
correct wavelengths. Let the height of the potential barrier be 0.75 eV, the energy of the
particle be 0.8 eV, and the width of the potential be $L = 0.5 \mu m$.