Thank you. How does this then relate back to the matrix representation? Would it just be ##\frac{1}{cos(\frac{\theta}{2})}\begin{pmatrix}cos^{2}(\frac{\theta}{2}) & e^{-i\phi}sin(\frac{\theta}{2})cos(\frac{\theta}{2}) \\ e^{i\phi}sin(\frac{\theta}{2})cos(\frac{\theta}{2}) &...
This didn't work. I got a factor of ##\frac{1}{cos^{2}(\frac{\theta}{2})}## when evaluating ##\langle\psi|\psi\rangle## with ##|\psi\rangle## being the output of SGn.
##
\begin{pmatrix}
cos^{2}(\frac{\theta}{2}) &
e^{-i\phi}sin(\frac{\theta}{2})cos(\frac{\theta}{2})
\end{pmatrix}...
Thanks for you help. I still don't see how ##\langle\,+\,n\,|+n\rangle## would give me the normalization factor though. I'm getting ##cos^{2}(\frac{\theta}{2}) + sin^{2}(\frac{\theta}{2}) = 1## which is what is expected.
So would ##\frac{1}{cos(\frac{\theta}{2})}## make for a suitable normalization factor? Is there a more formal way of determining this normalization factor?
Homework Statement
Given the series of three Stern-Gerlach devices:
Represent the action of the last two SG devices as matrices ##\hat{A}## and ##\hat{B}## in the ##|+z\rangle, |-z\rangle## basis.
Homework Equations
##|+n\rangle = cos(\frac{\theta}{2})|+z\rangle +...
Hey everyone!
Today's my first day here as an official member. I've visited the forums a couple times before but I've never posted anything. I'm a Junior at Northeastern University studying physics and electrical engineering. I'm taking quantum mechanics this semester which is the main reason...