A particle of charge e moves in a central potential V(r) superimposed onto a uniformmagnetic field B whose vector potential is A = B×r/2. (a) Show that if B is a weakfield, so that effects proportional to B2 can be neglected, then H(r, p) = p2/2m + V(r) − μ · B, where μ = (e/2mc) r × p. (b) Write down Hamilton’s equations in this approximation.
A particle of charge e moves in a central potential V(r) superimposed onto a uniformmagnetic field B whose vector potential is A = B×r/2. (a) Show that if B is a weakfield, so that effects proportional to B2 can be neglected, then H(r, p) = p2/2m + V(r) − μ · B, where μ = (e/2mc) r × p. (b) Write down Hamilton’s equations in this approximation.
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Question
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 H(r, p) = p2/
2m + V(r) − μ · B, where μ = (e/2mc) r × p. (b) Write down Hamilton’s equations in this approximation.
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