Quantum Hall Effect: Hamiltonian & Finding Solutions

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SUMMARY

The discussion centers on the Quantum Hall Effect and the derivation of its Hamiltonian, specifically the equation $$H= \frac {h^2}{2m} ( \delta_x^2+ (\delta_y+ \frac{iq}{h} B_x)^2)^2$$. A recommended resource for understanding this topic is the book edited by Prange and Girvin, which includes contributions from various experts in the field. Participants also discuss the relationship between the Hamiltonian and harmonic oscillators, emphasizing the importance of identifying conserved quantities within the system.

PREREQUISITES
  • Understanding of Quantum Mechanics principles
  • Familiarity with Hamiltonian mechanics
  • Knowledge of differential equations, particularly second-order
  • Basic concepts of condensed matter physics
NEXT STEPS
  • Study the book "The Quantum Hall Effect" edited by Prange and Girvin
  • Research Hamiltonian mechanics in the context of quantum systems
  • Learn about conserved quantities in quantum mechanics
  • Explore the mathematical techniques for solving second-order differential equations
USEFUL FOR

Physicists, graduate students in condensed matter physics, and researchers focusing on quantum mechanics and the Quantum Hall Effect will benefit from this discussion.

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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?


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