QuantumOperatorMethodsPretest

QuantumOperatorMethodsPretest - D The correct eigenvector...

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Quantum Operator Methods Pretest Name: _______________________________________ CU ID: ____________________ For the questions below, we will consider measurements on two observables, A and B, in a two-state system. Observable A has an associated operator ˆ A . ˆ A has two eigenvalues α 1 and 2 and eigenfunctions a 1 and a 2 respectively. Similarly, observable B has an associated operator, ˆ B which in turn has eigenvalues β 1 and 2 and eigenfunctions b 1 and b 2 respectively. We can write the eigenvector, b 1 , in terms of the eigenvectors of ˆ A : b 1 = 5 6 a 1 - 1 6 a 2 . Q1 : a) Which choice or choices below represent the eigenvector b 2 in terms of the eigenvectors of ˆ A ? I: 5 6 a 1 + 1 6 a 2 II: 1 6 a 1 - 5 6 a 2 III: 1 6 a 1 - i 5 6 a 2 A. One of these choices is correct B. More than one of these choices is correct C. None of these choices is correct
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Unformatted text preview: D. The correct eigenvector cannot be determinted from the information given b) Explain your answer. For each choice you selected as correct, explain how you know. If you stated that none of the choices are correct, give a correct choice. Finally, if a correct choice cannot be determined, state why. ©2010 Steve Goldhaber and the Physics Education Group University of Colorado at Boulder Q2: a) We measure A and obtain the value α 1 . If we now measure B, what is the probability we will obtain β 2 ? A. Zero B. 1 6 C. 5 6 D. one E. It cannot be determined b) Explain your answer. ©2010 Steve Goldhaber and the Physics Education Group University of Colorado at Boulder...
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  • Fall '08
  • STEVEPOLLOCK
  • Eigenvalue, eigenvector and eigenspace, Hilbert space, Eigenfunction, Physics Education Group, Education Group University

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QuantumOperatorMethodsPretest - D The correct eigenvector...

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