For a quantum particle in a scattering state as it interacts a certain potential, the general expressions for the transmission and reflection coefficients are given by Jref T = Jtrans Jinc R = Jinc (1) where Jinc, Jref, Jtrans are probability currents corresponding to the incident, reflected, and transmitted plane waves, respectively. (a) (2 pts) For the particle incident from the left to the symmetric finite square well potential -Vo-a<< a, show that V (x) = 0 ; elsewhere, T: = R = " A A Identify the incident, reflected and transmitted plane wave.

For a quantum particle in a scattering state as it interacts a certain potential, the general expressions for the transmission and reflection coefficients are given by Jref T = Jtrans Jinc R = Jinc (1) where Jinc, Jref, Jtrans are probability currents corresponding to the incident, reflected, and transmitted plane waves, respectively. (a) (2 pts) For the particle incident from the left to the symmetric finite square well potential -Vo-a<< a, show that V (x) = 0 ; elsewhere, T: = R = " A A Identify the incident, reflected and transmitted plane wave.