U1L5g.txt

#
# File:   content-mit-8370x-subtitles/U1L5g.txt
#
# Captions for course module
#
# This file has 27 caption lines.
#
# Do not add or delete any lines.  If there is text missing at the end, please add it to the last line.
#
#----------------------------------------

So now what I want to do is let's look at sigma z,
or Sz sigma z [? counter ?] I plus I [? counter ?] sigma z.
And consider a state, let's say 0 0 minus 1 1--

plus 1 1.

The expectation value of Sz on 0 0 plus 1 1 is 0.

1 0 0 minus 1, and this was 1 0 0 1 and 1 0 0 1--
1/2 probability-- is equal to 0.

But the actual, I guess, observable
is plus 1 with a probability 1/2,
minus 1 with probability 1/2.

Well, why?
Because it either projects it onto 0 0,
or it projects onto 1 1, or it projects it
onto the subspace consisting of 0 1 plus 1 0.

This vector does not overlap with that middle subspace.
So if you measure the spin on this state with respect
to the z-axis, you get plus one with probability 1/2, minus 1
with probability 1/2.
State 0 1 minus 1 0 get spin 0.