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1. Aparticleofmassmisinthestate m2 w (x, t) = Ae -a[(T)+it] where A and a are positive real constants. Find A. For what potential energy function V(X) does '4' satisfy the Schrodinger equation? Calculate the expectation values of x, x2. p. and p2. Find on and op. Is their product consistent with uncertainty principle? 9.0.0.9 2. A particle is represented (at time t = O) by the waveiunction Find the uncertainty in x (on). Find the uncertainty in p (op). . Check that the results are consistent with the uncertainty principle. A(a2 x2). ifan 5 +a til (it. 0) = 0. otherwise. a. Determine the normalization constant A. b. What is the expectation value of x (at time t = O)? c. What is the expectation value of p (at time t = 0)? d. Find the expectation value of x2. e. Find the expectation value of p2. t. g. 5