PX156 - D4 - classical and quantum particle

v = \sqrt{\frac{2 E}{m}}

v = \sqrt{\frac{2 (E - V_{0})}{m}}

for a quantum particle:
- if $E > V_{0} : λ$ increases
- if $E < V_{0} :$ small chance
probability of a quantum mechanical particle being reflected by a barrier for $E > V_{0} :$

\begin{aligned} k_{1} & = \frac{\sqrt{2 m E}}{ℏ} \\ k_{2} & = \frac{\sqrt{2 m (E - V_{0})}}{ℏ} \\ P & = {(\frac{k_{2} - k_{1}}{k_{2} + k_{1}})}^{2} \end{aligned}