The Hamiltonian for particle in an EM field is(adsbygoogle = window.adsbygoogle || []).push({});

H = 1/2m (p - qA)^2 + q phi

If we take the cross-terms, which corresponds to the paramagnetic term, we have

[tex]

H para = -q/2m * (p.A + A.p )

= iqh/2m * (\nabla .A + A.\nabla)

[/tex]

What I do not understand is how this simplifies into [tex] iqh/m * A.\nabla [/tex]?

assuming that [tex] \nabla .A = 0[/tex] (i.e. Coulomb gauge). Why does the factor of 1/2 disappears? I'm only a first year undergraduate and I'm learning this on my own. I will appreciate it if you give a fuller answer. Thank you.

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# Paramagnetic term of the hamiltonian

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