4. Consider a particle moving in one dimension under a potential barrier 0, V(x) = Vo 0, x < 0, 0 Vo, wave functions for each region can be expressed as 0,(x) = A elk x + Aje-ikx (x) = Azeik2x + Ase-ikzx Pu(x) = Azelka* + Ase-íkıx, where A'z = 0, assuming the incident particle is coming from x = -0. By imposing the boundary conditions, find the transmission and the reflection coefficients, 2 當 T= and R= A1 in terms of the parameters of the problem. Note that T + R = 1. For what values of I, the transmission coefficient T is maximized? What is the relation between those values and the wavelength in the second region? (b) For the case E < Vo, find the transmission coefficient T. Show that if 2m(V. -E) >> 1 h the transmission coefficient T, associated with the tunneling effect, can be approximated as 16E(V. -E) -21/2m(V. – E) T exp V. h Note that in the classical limit h→0, we have T → 0. This obviously means that the tunneling effect is a purely quantum effect.