- #1
ScotchDave
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The state [tex]\Psi[/tex] = [tex]\frac{1}{\sqrt{6}}[/tex][tex]\Psi[/tex]-1 + [tex]\frac{1}{\sqrt{2}}[/tex][tex]\Psi[/tex]1 + [tex]\frac{1}{\sqrt{3}}[/tex][tex]\Psi[/tex]2
is a linear combination of three orthonormal
eigenstates of the operator Ô corresponding
to eigenvalues -1, 1, and 2. What is the
expectation value of Ô for this state?
(A) 2/3
(B) [tex]\sqrt{\frac{7}{6}}[/tex]
(C) 1
(D) 4/3
(E) [tex]\frac{\sqrt{3} + 2\sqrt{2} - 1}{\sqrt{6}}[/tex]
[tex]<\hat{A}> = < \Psi |A|\Psi > = a < \Psi|\Psi > = a[/tex]
So using this eqn I get <[tex]\hat{O}[/tex]> = -1/6 + 1/2 + 2/3 = 1, this is the correct answer, but if someone could explain why this is correct I would appreciate it a lot.
is a linear combination of three orthonormal
eigenstates of the operator Ô corresponding
to eigenvalues -1, 1, and 2. What is the
expectation value of Ô for this state?
(A) 2/3
(B) [tex]\sqrt{\frac{7}{6}}[/tex]
(C) 1
(D) 4/3
(E) [tex]\frac{\sqrt{3} + 2\sqrt{2} - 1}{\sqrt{6}}[/tex]
[tex]<\hat{A}> = < \Psi |A|\Psi > = a < \Psi|\Psi > = a[/tex]
So using this eqn I get <[tex]\hat{O}[/tex]> = -1/6 + 1/2 + 2/3 = 1, this is the correct answer, but if someone could explain why this is correct I would appreciate it a lot.
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