Physics 125b – Problem Set 10 – Due Feb 3, 2009 Solutions

|x′ = v, y′ = u 〉 = |x = u, y = v 〉 . (1) We assume a similar relationship exists in momentum space (to be completely general, we should also include a possible phase factor, but for this problem it won’t be necessary): |px = a, py = b 〉 = |px = c, py = d 〉 . (2) Because the inner product in conserved under a change of coordinates, we have: 〈x′ = u, y′ = v |px = a, py = b 〉 = 〈x = u, y = v |px = a, py = b 〉 . (3) We use the position space coorespondence to rewrite the left side and expand the right side in the original basis: