spinors

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BemusedByQM - 14 Jul 2005 10:17 GMT

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
"

thanks

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Jim Heckman - 15 Jul 2005 21:05 GMT

On 14-Jul-2005, "BemusedByQM" <groover892002@yahoo.co.uk>
wrote in message <05qBe.3411$vz5.1067@newsfe4-win.ntli.net>:

> Hi,
>
[quoted text clipped - 8 lines]
> 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)?

Signature

Jim Heckman

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Natural Science Forum / Physics / Particle Physics / July 2005

spinors