Given a Hermitian operator Ä, any ket Ja), and a set off all eigenvectors of Ä (given by |A1), |A2), ... An)) such that these eigenvectors form an orthonormal basis. Show that the expectation value of  is equal to N (a|A|a) = > 2; P(A = A;) i=1 Consider: • A; is eigenvalue of  that corresponds to the ket |A;) • P(A = 1;) is the probability of measuring 2; if the quantum system is in the state |a)
Given a Hermitian operator Ä, any ket Ja), and a set off all eigenvectors of Ä (given by |A1), |A2), ... An)) such that these eigenvectors form an orthonormal basis. Show that the expectation value of  is equal to N (a|A|a) = > 2; P(A = A;) i=1 Consider: • A; is eigenvalue of  that corresponds to the ket |A;) • P(A = 1;) is the probability of measuring 2; if the quantum system is in the state |a)
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Hermitian operator
Transcribed Image Text:Given a Hermitian operator Ä, any ket |a), and a set off all eigenvectors of Ä (given by |A1), |A2), ... |AN)) such
that these eigenvectors form an orthonormal basis. Show that the expectation value of  is equal to
N
(a|A|a} = ; P(A = d;)
Consider:
A; is eigenvalue of  that corresponds to the ket |A;)
• P(A = 1;) is the probability of measuring 2; if the quantum system is in the state Ja)
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