Textbook: Mathematical Methods in Physical Sciences

a) Find the eigenvalues of A. 1. Let A = 2 5 4 b) Find the eigenvectors of A. 2. a) Let A, B be operators with [A, B] = I, where I is the identity operator. Find [A2, B]. b) Let A = 0/Ox, B = Top. (Here B is an OPERATOR: B takes a function f(x) to another function g(x) = xf(x).) Calculate [02/Ox2, Top] by comparing 02/Ox2(xf (x)) and x02/0x2f(x). c) Verify that your answer from b) agrees with the general formula from part a)