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BemusedByQM
science forum beginner
Joined: 11 Jul 2005
Posts: 49
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 Posted: Thu Jul 14, 2005 7:17 am Post subject:
spinors
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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
science forum Guru Wannabe
Joined: 28 Apr 2005
Posts: 121
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| Posted: Fri Jul 15, 2005 6:05 pm Post subject:
Re: spinors
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On 14-Jul-2005, "BemusedByQM" <groover892002@yahoo.co.uk>
wrote in message <05qBe.3411$vz5.1067@newsfe4-win.ntli.net>:
| Quote: | 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 "
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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 |
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