How to develop a method to reconstruct state in quantum mech

[john chen]

Hi all,
There is this question;

Firstly, I am new to quantum mechanics and there are a lot of terms I am unfamiliar with. So there is this question that asks me to develop a method to reconstruct state and I have no clue how I should start with. Any help or steps to solve this type of question is greatly appreciated..

 

[stevendaryl]

The question's a little unclear, but I assume that what the textbook wants you to do is to pick some quantities to measure, such as the z-component of the spin, and use the results of many measurements to compute the parameters $\alpha$ and $\beta$. Do you know what the connection is between $\alpha$ and $\beta$ and the results of a measurement of the z-component of the spin?

 

[stevendaryl]

Actually, this should be moved into the Homework forum.

 

[john chen]

The question's a little unclear, but I assume that what the textbook wants you to do is to pick some quantities to measure, such as the z-component of the spin, and use the results of many measurements to compute the parameters $\alpha$ and $\beta$. Do you know what the connection is between $\alpha$ and $\beta$ and the results of a measurement of the z-component of the spin?

Hi thanks for replying... this is my first time using this forum to ask questions relating to physics so I wasn't sure where to exactly post it anyways, I'm not sure what spin state component the question ask me to use like is it x,y or z?And also what is the meaning of alpha and beta? Like what should I do as such my answer becomes the meaning of alpha and beta?

 

[stevendaryl]

No offense, but it seems to me that you must have missed a critical lesson, if you don't know what $\alpha$ and $\beta$ are. What I'm assuming they mean is that your atoms have intrinsic spin $\frac{1}{2}$, and that the state is $\alpha |U_z\rangle + \beta |D_z\rangle$, where $|U_z\rangle$ and $|D_z\rangle$ are the states corresponding to spin-up and spin-down in the z-direction. When there are only finitely many possible states, they often use matrix notation, where $|U_z\rangle = \left( \begin{array} \\ 1 \\ 0 \end{array} \right)$ and $|D_z\rangle = \left( \begin{array} \\ 0 \\ 1 \end{array} \right)$.

I suggest that you go back and try to understand the pre-requisites for this question.