A particle of charge e moves in a central potential V(r) superimposed onto a uniform magnetic field B whose vector potential is A = B x r/2. (a) Show that if B is a weak field, so that effects proportional to B² can be neglected, then where p² H(r, p): = + V(r) - μ. B, 2m e 2mc (b) Write down Hamilton's equations in this approximation. μ = -rxp.
A particle of charge e moves in a central potential V(r) superimposed onto a uniform magnetic field B whose vector potential is A = B x r/2. (a) Show that if B is a weak field, so that effects proportional to B² can be neglected, then where p² H(r, p): = + V(r) - μ. B, 2m e 2mc (b) Write down Hamilton's equations in this approximation. μ = -rxp.
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Transcribed Image Text:7.10 A particle of charge e moves in a central potential V(r) superimposed onto a uniform
magnetic field B whose vector potential is A = B × r/2. (a) Show that if B is a weak
field, so that effects proportional to B² can be neglected, then
where
H(r, p):
p²
2m
+ V(r) − µ · B,
e
2mc
(b) Write down Hamilton's equations in this approximation.
μ =
-rxp.
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