Quantum Spin Measurement: Determining Input State and Probabilities

[Delong]

I have this take home I would like some help on thanks:
"The spin components of a beam of atoms prepared in the state |ψ>are measured and the following experimental probabilities are obtained:

P+z=1/2
P-Z=1/2
P+x=3/4
P-x=1/4

(i.e., if the beam of atoms goes through a single Stern-Gerlach setup in the x-direction, 3/4 of the particles are measured to have spin up in the x-direction and 1/4 of the particles are measured to have spin down in the x-direction.)

1. From the experimental data, determine the input state as a linear combination of |=>z and |->z (i.e. determine as much of each coefficient of the two states in the sum). Show your work. With no lossof generality, you may assume that the coefficient of |+>z is real but the coefficient of |->z is not.

2. Determine P+y and P-y."


here's my attempt: the linear combination I got is 1/(2)^1/2 for |+>z and -i/(2)^1/2 for |->z. Not sure where to go from there. Thanks for any help I can get!

 

[berkeman]

I have this take home I would like some help on thanks:
"The spin components of a beam of atoms prepared in the state |ψ>are measured and the following experimental probabilities are obtained:

P+z=1/2
P-Z=1/2
P+x=3/4
P-x=1/4

(i.e., if the beam of atoms goes through a single Stern-Gerlach setup in the x-direction, 3/4 of the particles are measured to have spin up in the x-direction and 1/4 of the particles are measured to have spin down in the x-direction.)

1. From the experimental data, determine the input state as a linear combination of |=>z and |->z (i.e. determine as much of each coefficient of the two states in the sum). Show your work. With no lossof generality, you may assume that the coefficient of |+>z is real but the coefficient of |->z is not.

2. Determine P+y and P-y."


here's my attempt: the linear combination I got is 1/(2)^1/2 for |+>z and -i/(2)^1/2 for |->z. Not sure where to go from there. Thanks for any help I can get!

What do you mean by "take home"? Is this question from a take-home exam? If so, are you allowed to ask for tutorial help on the Internet for the exam?

 

[Delong]

It's a take home quiz. I'm don't know if I'm allowed or not but my professor never said anything against it so here I am.

 

[berkeman]

It's a take home quiz. I'm don't know if I'm allowed or not but my professor never said anything against it so here I am.

We don't generally help with take-home exams. If you can get an e-mail from the professor, you can PM it to me.

 

[once_more]

It's actually a question from Quantum Mecahnics by David McIntyre and I'd love some direction.

 

[berkeman]

It's actually a question from Quantum Mecahnics by David McIntyre and I'd love some direction.

Welcome to the PF.

So it doesn't look like (based on how old this thread is) the OP had permission to get help on his exam question. If you'd like help with the textbook question, please go ahead and start a new thread here in the Homework Help, Advanced Physics forum, and fill out the HH Template that you are provided. You should get good help as long as you show your efforts.