Unformatted text preview: a = i 1 2 2 i 3 b = i 1 2 3 (a) Construct a and b in terms of the dual basis 1 , 2 , 3 (b) Find a b and b a , and show that b a = a b (c) Find all nine matrix elements of the operator A = a b in this basis. (d) Show whether the operator A is Hermitian or not. 4. Consider a threedimensional ket space where operator B is defined as B = [ b ib ib ] (a) Find the eigenvalues and eigenvectors of operator B . (b) Find the matrix representation of operator B with respect to the vector basis given by its eigenvectors....
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 Fall '08
 Vachon
 Linear Algebra, mechanics, Hilbert space, Hermitian, Hermitian Operators

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