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 Â. A has two eigenvalues a₁ and a₂ and eigenvectors |a₁) and a₂) respectively. Similarly, observable B has an associated operator, B which in turn has eigenvalues and ₂ and eigenvectors b) and b₂) respectively. We can write the eigenvector, b₁), in terms of the eigenvectors of A: 16₂) = √5 (19₁) - √ las). Q1: a) Which choice or choices below represent the eigenvector b₂) in terms of the eigenvectors of Â? I: + II: √elas) - √olas) 1: √ √|19₁) - √ √ √192₂) (1/a) 5₁ III: A. One of these choices is correct B. More than one of these choices is correct C. None of these choices is correct 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.

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 Â. A has two eigenvalues a₁ and a₂ and eigenvectors |a₁) and a₂) respectively. Similarly, observable B has an associated operator, B which in turn has eigenvalues and ₂ and eigenvectors b) and b₂) respectively. We can write the eigenvector, b₁), in terms of the eigenvectors of A: 16₂) = √5 (19₁) - √ las). Q1: a) Which choice or choices below represent the eigenvector b₂) in terms of the eigenvectors of Â? I: + II: √elas) - √olas) 1: √ √|19₁) - √ √ √192₂) (1/a) 5₁ III: A. One of these choices is correct B. More than one of these choices is correct C. None of these choices is correct 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.