Intrinsic spin stern-gerlach application

[physics2004]

find the following:

if a particle (s=1/2) is prepared such that it is in the spin up state |f>=|z+>

what do the following mean? [<f|(Sz - <z+|Sz|f>1)^2|f>]^½ and
[<f|(Sx - <f|Sx|f>1)^2|f>]^½


The middle term sandwiched between the states is squared and the whole term being square rooted.

my guess: For the first one the measurement is repeated knowing the particle is in state |z>, you measure Sz- (which should be zero, but that's not what iam getting) so iam kind of lost.

 

[diazona]

If I rewrite the first formula as
$$\sqrt{\langle(S_z - \langle S_z \rangle)^2\rangle}$$
do you recognize that expression?

 

[physics2004]

uncertainty principle?

 

[someguy61]

after that use eqn 2.65 from desai textbook

 

[diazona]

uncertainty principle?

It's related to that, yes. Actually that is an expression for the uncertainty, or more precisely the standard deviation.

Is that what you meant?

 

[someguy61]

i guess they want you to show that there is an uncertainty when measuring the spin. U cannot measure the spin simultaneously in both x and z axis