- #1

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- Homework Statement
- Given an unnormalized spin state

##\Psi=(1+i)|+>-(1+i\sqrt{3})|->##

which direction does this spin point to?

- Relevant Equations
- ##|n;+> = cos\frac{\theta}{2}|+>+sin\frac{\theta}{2}e^{i\phi}|->##

From the relevant equation above, there is not imaginary part in the |+> state, so I multiplied the state by (1-i). The state is then :

##\Psi=(2)|+>-(1+\sqrt{3})+i(\sqrt{3}-1)|->##

Then I normalize it :

##\Psi=(\frac{1}{\sqrt{3}})|+>-\frac{1}{2\sqrt{3}}(1+\sqrt{3})+i(\sqrt{3}-1)|->##

From the |n;+> equation above, I concluded from the |+> part that :

##cos\frac{\theta}{2}=\frac{1}{\sqrt{3}}##

But when I did the same thing from the |-> part, I got different value from ##cos\frac{\theta}{2}##

My guess is that this method of determining direction of spin state is probably wrong.

Edit: Somehow the Latex is not working, I'm trying to figure out how to fix this

##\Psi=(2)|+>-(1+\sqrt{3})+i(\sqrt{3}-1)|->##

Then I normalize it :

##\Psi=(\frac{1}{\sqrt{3}})|+>-\frac{1}{2\sqrt{3}}(1+\sqrt{3})+i(\sqrt{3}-1)|->##

From the |n;+> equation above, I concluded from the |+> part that :

##cos\frac{\theta}{2}=\frac{1}{\sqrt{3}}##

But when I did the same thing from the |-> part, I got different value from ##cos\frac{\theta}{2}##

My guess is that this method of determining direction of spin state is probably wrong.

Edit: Somehow the Latex is not working, I'm trying to figure out how to fix this

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