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Quantum Mechanics with Basic Field Theory by Bipin R. Desai

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12 Landau levels and quantum Hall effect

In this chapter we consider the motion of a charged particle in a magnetic field. This is intrinsically a three-dimensional problem but for a charged particle in a uniform magnetic field it can be recast as a two-dimensional problem since the particle acts as a free particle in the direction of the magnetic field, while in the plane perpendicular to the magnetic field the particle’s motion can be described in terms of an equivalent two-dimensional harmonic oscillator. It is found that when charged particles are subjected to a magnetic field their orbital motion is quantized. Thus the particles can only occupy orbits with discrete energy eigenvalues called Landau levels named after the physicist Lev Landau. ...

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