Question: 1. (a) Consider the matrix (0 0 1 N= 0 00 100 i. Is it Hermitian? ii. Find its eigenvalues and eigenvectors? iii. Are

1. (a) Consider the matrix (0 0 1 N= 0 00 100

1. (a) Consider the matrix (0 0 1 N= 0 00 100 i. Is it Hermitian? ii. Find its eigenvalues and eigenvectors? iii. Are they orthogonal? iv. Verify that U'QU is diagonal, U being the matrix of eigenvectors of 2? (b) You are given the following operators: Or6(z) = r*v(x), Solve the eigenvalue problem z(x) = Ap(x). Also calculate the commutators

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