Conjugate momentum in the hamiltonian

[moobox]

Hey,

I just have a quick question that I haven't quite been able to find a definitive answer to, regarding conjugate momenta in the Hamiltonian.

Ok, so it regards the following term for the hamiltonian in a magnetic field:

H=\frac{1}{2m}(p-qA)^2

I'd like to ask whether p is the conjugate momentum or if p_c=p-qA is the conjugate momentum. As a guess, I would say that p_c=p-qA is the conjugate momentum, as it seems to me that the hamiltonian should take into account the magnetic field. Would this then mean that the hamiltonian could be written as H=\frac{1}{2m}(p_c)^2

Also, very important, does -i\hbar\nabla represent the canonical momentum operator or the classical/mechanical momentum operatpor?

Im sure the answers are around somewhere on the internet, but it strikes me that there are some conflicting statements and a tendency to just go "oh yeah, now we swap the canonical momentum, p for mechanical momentum p" and the like, so it would be nice to get a definitive answer.

Thanks for your help!

 

[genneth]

p is the conjugate/canonical momentum. p-eA is the mechanical momentum.

 

[moobox]

Ah, brilliant! Thanks for your quick response!

So that would make i\hbar\nabla the conjugate/canonical momentum operator?