Question

1) (20 pts.) Consider a scattering process with a potential V(x) which goes to zero as too, but is otherwise not specified (so for instance, don't assume that V() is a constant anywhere). The wavefunction has the following limits as a too: (3) elke + reiki for- for r kr + If r=0.8, what is 14? (Hint: Use the probability current to write R and T in terms of rand 1.)

Answer 1

ik x ikx ) # # 4x) = { eikety reike tre I teikx je 7) = { you get there? ikx tr ike -ika. le + Ye 2 m L iky * le tre * * e . tri 020 U$ (3,0) = in s velk velky a vir diet) -le* y* cita) 2 (reiks)? * {1-14"} je last) eine tolle is). **() - tk itt? 0; +) = 1, 0+,+) => ** {1-171*}*tej x m 2 Ir+11 = 1 R + T = 1

If Irl=.8 = 1+1=1 - .64 = 36 It) = .6 R=181², T=1t1² if you * Please have let me know any questions!