Repeated Measurements Homework: True or False?

[daveyman]

Homework Statement

This is a true or false question on a practice test. I'm having a hard time making sense of it. Here it is:

Two operators A and B do not share eigen states a(n) and b(n) where n=1,2,3,etc. A measurement of A is made and the system is found to be in state a(1). If the measurement of A is repeated at some later time, and if A does not commute the Hamiltonian H, the system may be found to be in a state other than a(1) (True or False).

Homework Equations

N/A

The Attempt at a Solution

My guess is true, but I'm not sure how the phrase about the Hamiltonian plays into this.

Thanks for your help!

 

[olgranpappy]

Homework Statement

This is a true or false question on a practice test. I'm having a hard time making sense of it. Here it is:

Two operators A and B do not share eigen states a(n) and b(n) where n=1,2,3,etc. A measurement of A is made and the system is found to be in state a(1). If the measurement of A is repeated at some later time, and if A does not commute the Hamiltonian H, the system may be found to be in a state other than a(1) (True or False).

Homework Equations

N/A

The Attempt at a Solution

My guess is true, but I'm not sure how the phrase about the Hamiltonian plays into this.

Thanks for your help!

The hamiltonian play a role because it determines how the state changes with time.

 

[daveyman]

So, since the two operators do not commute, that means the state is changing with time, correct? This definitely means the answer is true.

Please correct me if I am wrong - thanks!