Problem 3.33 Sequential measurements. An operator Â, representing observable A, has two (normalized) eigenstates j and 2, with eigenvalues aj and a2, respectively. Operator §, representing observable B, has two (normalized) eigenstates ø1 and 02, with eigenvalues bị and bɔ. The eigenstates are related by VI = (3ø1 + 402)/5, 2 = (461 – 3¢2) /5. %3D (a) Observable A is measured, and the value a] 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? (Note that the answer would be quite different if I had told you the outcome of the B measurement.)
Problem 3.33 Sequential measurements. An operator Â, representing observable A, has two (normalized) eigenstates j and 2, with eigenvalues aj and a2, respectively. Operator §, representing observable B, has two (normalized) eigenstates ø1 and 02, with eigenvalues bị and bɔ. The eigenstates are related by VI = (3ø1 + 402)/5, 2 = (461 – 3¢2) /5. %3D (a) Observable A is measured, and the value a] 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? (Note that the answer would be quite different if I had told you the outcome of the B measurement.)
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![Problem 3.33 Sequential measurements. An operator Â, representing observable
A, has two (normalized) eigenstates j and 2, with eigenvalues aj and a2,
respectively. Operator §, representing observable B, has two (normalized)
eigenstates ø1 and 02, with eigenvalues bị and bɔ. The eigenstates are related
by
VI = (3ø1 + 402)/5, 2 = (461 – 3¢2) /5.
%3D
(a) Observable A is measured, and the value a] 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? (Note that the answer would be quite different if
I had told you the outcome of the B measurement.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f916f44-2b56-40b3-9b96-44e026d40d84%2F7955323d-ce98-4147-86c9-605717f0cd2c%2Fye4qxwo_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 3.33 Sequential measurements. An operator Â, representing observable
A, has two (normalized) eigenstates j and 2, with eigenvalues aj and a2,
respectively. Operator §, representing observable B, has two (normalized)
eigenstates ø1 and 02, with eigenvalues bị and bɔ. The eigenstates are related
by
VI = (3ø1 + 402)/5, 2 = (461 – 3¢2) /5.
%3D
(a) Observable A is measured, and the value a] 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? (Note that the answer would be quite different if
I had told you the outcome of the B measurement.)
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