A free particle with energy E hits a potential step with $U_0 > 0$ at $x \geq 0$. Assume that $E > U_0$.

(1) Determine the wavelengths associated with the particle in the area $x > 0$ and in the area $x < 0$.

(2) What is the relationship between the amplitude of the transmitted wave in the area $x > 0$ and the amplitude of the incident wave in the area $x < 0$.

Use the two boundary conditions that at $x=0$

$$

\Psi_{x<0} = \Psi_{x>0}

$$

$$

({\dfrac{\partial\Psi_{x<0}}{\partial_x}})_{x=0} = ({\dfrac{\partial\Psi_{x>0}}{\partial_x}})_{x=0}

$$

Thanks in advance