Consider the ket Ja) and an operator Â, a bra vector that corresponds to the ket Âla) is (a|† where Ât is a Hermitian operator adjoint to Â. *Note: *The operator acts on the bra vectors from right to left. *Ja) is any arbitrary ket from the vector space V (of dimension N). *The operators  is any linear operators acting on vectors from V. *The set of all eigenvectors of  forms an orthonormal basis. a) Show that the eigenvalues of a Hermitian operator  is real. b) Show that the eigenvectors of a Hermitian operator Ä are orthogonal to each other.
Consider the ket Ja) and an operator Â, a bra vector that corresponds to the ket Âla) is (a|† where Ât is a Hermitian operator adjoint to Â. *Note: *The operator acts on the bra vectors from right to left. *Ja) is any arbitrary ket from the vector space V (of dimension N). *The operators  is any linear operators acting on vectors from V. *The set of all eigenvectors of  forms an orthonormal basis. a) Show that the eigenvalues of a Hermitian operator  is real. b) Show that the eigenvectors of a Hermitian operator Ä are orthogonal to each other.
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Transcribed Image Text:Consider the ket Ja) and an operator Â, a bra vector that corresponds to the ket Âla) is (a|† where Ât is a Hermitian operator
adjoint to Â.
*Note:
*The operator acts on the bra vectors from right to left.
*Ja) is any arbitrary ket from the vector space V (of dimension N).
*The operators Ä is any linear operators acting on vectors from V.
*The set of all eigenvectors of  forms an orthonormal basis.
a) Show that the eigenvalues of a Hermitian operator A is real.
b) Show that the eigenvectors of a Hermitian operator Ä are orthogonal to each other.
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