# Journal of Operator Theory

Volume 37, Issue 1, Winter 1997 pp. 183-194.

Anticommutativity of spin 1/2 Schrodinger operators with magnetic fields**Authors**: Osamu Ogurisu

**Author institution:**Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060, JAPAN

**Summary:**It is proven that the spin 1/2 SchrÃ¶dinger operator $\tilde H$ with a constant magnetic field is the square of a sum of mutually strongly anticommuting self-adjoint operators. As an application, by using this formula, the essential spectrum of $\tilde H$ with a vector potential in a class is identified. The class contains a vector potential to which Shigekawaâ€™s theorem (I. Shigekawa, J. Funct. Anal. 101(1991), 255-285) cannot be applied.

Contents Full-Text PDF