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Assume the operators Ä and B commute with each other, show that c) The eigenvalues of B are given by (A;|B|A;)

Assume the operators Ä and B commute with each other, show that c) The eigenvalues of B are given by (A;|B|A;)

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Assume the operators Ä and B commute with each other, show that c) The eigenvalues of B are given by (A;|B|A;) Consider that: • la) is an arbitrary ket from the vector space V • operators Ä and B are linear operators acting on vectors from V • the set of all eigenvectors of  is given by |A1), A2), ... |AN), and form an orthonormal basis A¡j and Bij are matrix elements of the matrix representations of the operators A and B
Transcribed Image Text:Assume the operators Ä and B commute with each other, show that c) The eigenvalues of B are given by (A;|B|A;) Consider that: • la) is an arbitrary ket from the vector space V • operators Ä and B are linear operators acting on vectors from V • the set of all eigenvectors of  is given by |A1), A2), ... |AN), and form an orthonormal basis A¡j and Bij are matrix elements of the matrix representations of the operators A and B
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