A 2D Harmonica Oscillator For Holes In Magnetic Field

Hello

I am bemused by a sign convention for Holes, My questions are as follow:

For an electron inside the 2D Circular Quantum Well. We can write our Hamiltonian as

H = 1/2m * ( p - q A)^2 + 1/2 m w^2 r^2 (Should we use minus in the momentum term? I think for Holes, it is)

If we expand this Hamiltonian under gauge A = -B/2 (y,x,0), we will obtain a effective 2D Harmonica Oscillator with a extra term :

H = 2D-Harmonica Oscillator - w_c/2 l_z (This sign is confusing)

where l_z is the angular momentum operators in z direction.
My question is, are the two minus signs make sense in my equations?

I am not too sure if it is correct because I have seen some literature get a total different sign, And this will affect the spectrum of the hole.

Thanks!
 
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