Electron on a Surface in an External Magnetic Field: Hidden Supersymmetry, Zero Modes and Boundary Conditions

  • Yu. A. Sitenko
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)


The ideas of supersymmetry [1,2,3] have deeply influenced various trends of modern theoretical physics. In this respect attention should be paid to the patterns of a possible realization of supersymmetry, as intrinsic symmetry in quantum mechanical systems. In particular, the well-known problem of the electron motion in external static homogeneous magnetic field [4] can be reduced to the problem of the supersymmetry harmonic oscillator (see, for example, the review [5]). As it has been shown in Ref. [6] supersymmetry is also present in the case of inhomogeneous magnetic field with parallel force lines. The latter case corresponds to the supersymmetric quantum mechanics describing the interaction among the bosonic degrees of freedom (coordinates in the plane orthogonal to the direction of magnetic field) and the fermionic degree of freedom (spin).


Zero Mode Index Theorem Compact Surface Inhomogeneous Magnetic Field Supersymmetric Quantum Mechanic 
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Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • Yu. A. Sitenko
    • 1
  1. 1.Institute for Theoretical PhysicsKievUSSR

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