Re: spinors


On 14-Jul-2005, "BemusedByQM" <groover892002@xxxxxxxxxxx>
wrote in message <05qBe.3411$vz5.1067@xxxxxxxxxxxxxxxxxxxx>:

> Hi,
>
> Wondering if any of you can point me in the right direction in
> answering this:-
>
> "Initially at t = 0 an electron is in an eigenstate of Sx with
> eigenvalue hbar/2 (that reads plancks constant with a 'bar' through
> it) . The magnetic field has magnitude B and direction specified by
> the spherical polar angles theta = pi/3 and phi = pi/2
>
> Write down a spinor a0 that represents the electrons spin state at
> time t =0 "

The direction of the electron's spin precesses uniformly around the
direction of the external magnetic field. I forget the exact formula
for the rate of precession, but surely it's proportional both to B and
to the magnitude of the electron's magnetic moment -- probably to the
magnitude of the cross product of the two vectors.

Do you know how to express the components of a vector that precesses
around another fixed vector? (Hint: First express the precessing vector
as the sum of a vector parallel to, and a vector perpendicular to, the
fixed vector.)

Do you know how to express the components of a spin-1/2 spinor that
'points' in a given direction (theta, phi)?

--
Jim Heckman
.