On the Nonrelativistic 2D Purely Magnetic Supersymmetric Pauli Operator

Abstract

The Complete Manifold of Ground State Eigenfunctions for the Purely Magnetic 2D Pauli Operator is considered as a by-product of the new reduction found by the present authors few years ago for the Algebrogeometric Inverse Spectral Data (i.e. Riemann Surfaces and Divisors). This reduction is associated with the (2+1) Soliton Hierarhy containing a 2D analog of the famous "Burgers System". This article contains also exposition of the previous works made since 1980 including the first topological ideas in the space of quasimomenta. We present here also new results dedicated to the self-adjoint boundary problems for Pauli Operator. The 2D zero level "nonspectral" Bloch-Floquet functions give discrete points of additional spectrum similar to the "boundary states" of finite-gap 1D potentials in the gaps.

39 pages, 10 figures, In the latest version discussion on topology studies of the quasimomenta space made by Russian school since 1980 is added. Survey part of this article dedicated to the boundary conditions is also increased. The list of references was essentially extended