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If you upload an image please make sure your answers are clear and your writing is legible. Please print your answers and do not write in script or cursive.

Consider the Hamiltonian.

and the state

b. Consider another operator A associated with an observable. Expressed in the same basis as above.

If at time t = 0 the particle is measured for observable A and found to have the value 3a, will another measurement of this observable also be 3a for any time t later? Explain.

If you upload an image please make sure your answers are clear and your writing is legible. Please print your answers and do not write in script or cursive. Consider the Hamiltonian. and the state a. If at a time t = 0 the particle begins state |psi >, will it remain in that state at any time t later? Explain. b. Consider another operator A associated with an observable. Expressed in the same basis as above. If at time t = 0 the particle is measured for observable A and found to have the value 3a, will another measurement of this observable also be 3a for any time t later? Explain.

Explanation / Answer

a) so a state wil remain constant if it is an eigenvalue of H

so H psi = (2 5i   (i    (2i + 5i     (7i 7 (i
        -5i 2) 1) = -5i^2 + 2) = 7) =    1)

so it is an eigenvector with eigenvalue 7

so it wil remaine in that state

b)

Since it is diagonal it has eigenvalues a and 3a, with eigenvecotr (10) and(0 1)

so if it is in state with value 3a that means it at an eigenvector (0 1)

so it will stay the same

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