‏صورة من احمد مرتضى Exercise 2.19Consider the matrixA-( 96 )=(a) Find the eigenvalues and the normalized eigenvectors for the matrix A.CHAPTER 2. MATHEMATICAL TOOLS OF QUANTUM MECHANICS(b) Do these eigenvectors form a basis (i.e., is this basis complete and orthonormal)?(c) Consider the matrix U which is formed from the normalized eigenvectors of A. Verifythat U is unitary and that it satisfies1580-(%).0UT AU =where 1 and 2 are the eigenvalues of A.(d) Show that ex = cosh x 4 sinh x.

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Answered: 503 (b) Do these eigenvectors form a…

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503 (b) Do these eigenvectors form a basis (i.e., is this basis complete and orthonormal)? (c) Consider the matrix U which is formed from the normalized eigenvectors of A. Verify that U is unitary and that it satisfies 0 UT AU = (2/2). 0