Quantum Hall Effect: Hamiltonian & Finding Solutions

[clumps tim]

Hi , I need a good book or lecture on quantum hall effect.

my supervisor wants me to find the Hamiltonian for the Qunatum hall effect, he want me to find this from this relation if it looks like a 2nd order differential of harmonic oscillation. can you please guide me doing this?


$$H= \frac {h^2}{2m} ( \delta_x^2+ (\delta_y+ \frac{iq}{h} B_x)^2)^2$$

 

[king vitamin]

A great book is this one edited by Prange and Girvin, with a lot of good chapters by experts. There are a few more books/reviews that I can think of, but I think this is a good one for an intro. Many modern condensed matter books will have an intro too.

For the Hamiltonian you posted: do you see any conserved quantities? Can you find a way to relate it to a harmonic oscillator Hamiltonian?