Semi-classical spectrum of integrable systems in a magnetic field

Abstract

The quantum dynamics of an electron in a uniform magnetic field is studied for geometries corresponding to integrable cases. We obtain the uniform asymptotic approximation of the WKB energies and wavefunctions for the semi-infinite plane and the disc. These analytical solutions are shown to be in excellent agreement with the numerical results obtained from the Schrodinger equations even for the lowest energy states. The classically exact notions of bulk and edge states are followed to their semi-classical limit, when the uniform approximation provides the connection between bulk and edge.

17 pages, Revtex, 6 figures

References in corpus (3)

• Quantum localization in rough billiards
• Periodic Orbit Theory of the circular billiard in homogeneous magnetic fields
• Localization in a rough billiard: A sigma model formulation

Cited by in corpus (4)

• The boundary integral method for magnetic billiards
• Quantum-information theory of magnetic field influence on circular dots with different boundary conditions
• Rotational Symmetry Protected Edge and Corner States in Abelian topological phases
• Current distribution in magnetically confined 2DEG: semiclassical and quantum mechanical treatment