This isn't a homework problem - I can't understand a particular statement in my professor's notes. As such, I hope it's in the correct forum.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

The Hamiltonian for a charged particle in a potential fieldAis

[itex]\hat{H}[/itex] = (1/2m) ( -i [itex]\hbar[/itex] [itex]\nabla[/itex] - qA)[itex]^{2}[/itex]

The square bracket can be expanded.

2. Relevant equations

In my professor's notes, this expands to [itex]\hat{H}[/itex] = (1/2m) ( -[itex]\hbar[/itex][itex]^{2}[/itex][itex]\nabla[/itex][itex]^{2}[/itex] + q[itex]^{2}[/itex]A[itex]^{2}[/itex] + 2 q i [itex]\hbar[/itex]A[itex]\bullet \nabla[/itex]+ q i [itex]\hbar[/itex] ([itex]\nabla \bullet [/itex] A)

3. The attempt at a solution

When I attempt the expansion myself, I don't get the factor of 2 present in the 3rd term of the expansion. I know that it must be there - subsequent proofs using the Landau gauge don't work without it - but I don't understand where it came from.

Any help in understanding the reasoning behind this would be greatly appreciated.

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# Expanding the electromagnetic hamiltonian

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