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## Main Question or Discussion Point

I am a little stuck understanding and answering the following questions. Can anyone help me with them?

"A system has four eigenstates of an observable, with corresponding eigenvalues 3/2, 1/2, -1/2 and -3/2, and normalized eigenfunctions

Psi_{3/2}, Psi_{1/2}, Psi_{-1/2} and Psi_{-3/2} respectively. (cant get tex to work properly)

Measurements of the observable are made on three systems that are all in the same superposition state, and yield the values 3/2, -1/2 and -3/2"

1)What can you say about the state of the system after each measurement?

2)What can you say about the original superposition state?

3)If many measurements on systems that are all in the same superposition state never yield the result -1/2, and give the result 3/2 twice as often as the other two possible results, deduce the normalized form of the superposition state

4)What is the expectation value of the observable in this state?

"A system has four eigenstates of an observable, with corresponding eigenvalues 3/2, 1/2, -1/2 and -3/2, and normalized eigenfunctions

Psi_{3/2}, Psi_{1/2}, Psi_{-1/2} and Psi_{-3/2} respectively. (cant get tex to work properly)

Measurements of the observable are made on three systems that are all in the same superposition state, and yield the values 3/2, -1/2 and -3/2"

1)What can you say about the state of the system after each measurement?

2)What can you say about the original superposition state?

3)If many measurements on systems that are all in the same superposition state never yield the result -1/2, and give the result 3/2 twice as often as the other two possible results, deduce the normalized form of the superposition state

4)What is the expectation value of the observable in this state?