Question

Professor A Abdurrahman's Course on Quantum Mechanics Quantum Mechanics I- Problem Set No. 3 Due to 04/30/2018. Late homework will not be accepted. Problem 1 Prove that Hint. Direct computation. Problem 2 We have been dealing with real potential V (x) so far so now suppose that V (a) is complea. Compute dt Problem 3 For the Gaussian a) 1 /4 Compute (a) (z") for all alues of n integer, and (b) Compute fors(x) given above. Hint: ? ?-V(a2)-(x)2 Problem 4 (a) Find the wave function in the momentum space ( for the Gaussian given in the previous problem and use ? (p) to com pute (") for all values of n integer, (b) Compute Ap using the rek tion,Ap = \/ (p2)-(P)2 and use the result unth that for Av comput in the previous problem to compute the product ?x ?p Problem 5 Prove the following operator identitsy roblem 6 Suppose you are given a function ?(0), where-1-e an angular variable. For the boundary condition (T) ow that the expectation value (L) is real, where the operator fined by

problem 2

Answer 1

a) Solu ?웃 2m っ거.. 木 p (21, 4) 2オ 2 m つナ ホ gオ

大 9- ) 17 14.