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Unformatted text preview: ) ( ) ~ ( | ~ * * 2 * 1 * n T v v v v v v L = = =< The Inner Product: The norm of a state is <v|v> = |v 1 | 2 +|v 2 | 2 +...+|v n | 2 . The Unit Matrix: The unit matrix takes every vector into itself. = 1 1 1 L M M M M L L I ( i.e. I ij = ij ) Orthogonal and Unitary: A matrix O is orthogonal if O-1 = O T and a matrix U is unitary if U-1 = U : OO T = O T O = 1 UU = U U = 1. Not all operators can be expressed in terms of functions and differentials! Ket vector! Bra vector! Orthogonal Unitary...
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- Spring '07