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Suppose you have an observable N with three eigenvalues 4, 8, and -1, with orthonormal eigenvectors 1), 2), and |3), respectively. A quantum iv3 V5 particle in state |) = ÷|1) – V 2) + |3). Use this information to - 3 3 answer the following questions. What is (N)? 3 11 3 23 9

Suppose you have an observable N with three eigenvalues 4, 8, and -1, with orthonormal eigenvectors 1), 2), and |3), respectively. A quantum iv3 V5 particle in state |) = ÷|1) – V 2) + |3). Use this information to - 3 3 answer the following questions. What is (N)? 3 11 3 23 9

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Suppose you have an observable \( \Omega \) with three eigenvalues 4, 8, and -1, with orthonormal eigenvectors \( |1\rangle, |2\rangle, \) and \( |3\rangle, \) respectively. A quantum particle in state \[ |\psi\rangle = \frac{i}{3} |1\rangle - \frac{i\sqrt{3}}{3} |2\rangle + \frac{\sqrt{5}}{3} |3\rangle \] Use this information to answer the following questions. What is \( \langle \Omega \rangle \)? - ○ 3 - ○ 0 - ○ \(\frac{11}{3}\) - ○ \(\frac{23}{9}\)
Transcribed Image Text:Suppose you have an observable \( \Omega \) with three eigenvalues 4, 8, and -1, with orthonormal eigenvectors \( |1\rangle, |2\rangle, \) and \( |3\rangle, \) respectively. A quantum particle in state \[ |\psi\rangle = \frac{i}{3} |1\rangle - \frac{i\sqrt{3}}{3} |2\rangle + \frac{\sqrt{5}}{3} |3\rangle \] Use this information to answer the following questions. What is \( \langle \Omega \rangle \)? - ○ 3 - ○ 0 - ○ \(\frac{11}{3}\) - ○ \(\frac{23}{9}\)
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Step 1

Expectation value of the given observable

Ω=<ψΩψ>=c1*<1+c2*<2+c3*<3Ωc11>+c22>+c33>=c1*c1<1Ω1>+c2*c2<2Ω2>+c3*c3<3Ω3>

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