 #1
Foracle
 30
 8
 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 (1i). 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
Last edited: