Sequential measurements An operator A, representing observable A, has two (normalized) eigenstates 1 and 2 , with eigenvalues 1 and 2 , respectively Operator B, representing observable B, has two (normalized) eigenstates 1 and 2 , with eigenvalues b 1 and b 2 The eigenstates are related by (a) Observable A is measured, and the value is obtained What is the state of the system (immediately) after this measurement (b) If B is now measured, what are the possible results, and what are their probabilities (c) Right after the measurement of B, A is measured again What is the probability of getting a 1 V1 (301 402) 5, 2 (401 302) 5

Question: Sequential measurements. An operator A, representing observable A, has two (normalized) eigenstates 1 and 2 , with eigenvalues 1 and 2

Sequential measurements. An operator Â, representing observable A, has two (normalized) eigenstates Ψ₁ and Ψ₂, with eigenvalues α₁ and α₂, respectively. Operator B̂, representing observable B, has two (normalized) eigenstates ∅₁ and ∅₂, with eigenvalues b₁ and b₂. The eigenstates are related by

V1 = (301 +402)/5, 2= (401 - 302)/5. (a) Observable A is measured, and the value is obtained. What is the state of the system (immediately) after this measurement?
(b) If B is now measured, what are the possible results, and what are their probabilities?
(c) Right after the measurement of B, A is measured again. What is the probability of getting a₁?

V1 = (301 +402)/5, 2= (401 - 302)/5.

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