An algebraic approach to Saxon-Hutner theorem. (English) Zbl 1192.81133

Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 292-300 (2008).
Summary: Here we give some necessary and sufficient conditions for the validity of the Saxon-Hutner conjecture concerning the preservation of the energy gaps into an infinite one-dimensional lattice.
For the entire collection see [Zbl 1154.17001].


81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
22E70 Applications of Lie groups to the sciences; explicit representations
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
82D25 Statistical mechanics of crystals