Monodromy of Schrödinger Operators

Abstract

This chapter – which makes use of the objects and concepts introduced in Chap. 8 – is mainly concerned with the determination of the monodromy of Schrödinger operators in ${\mathcal{S}}_{\leq 2}^{\mathit{aff }} :=\{ -2\mathrm{i}{\partial }_{t} - {\partial }_{r}^{2} + {V }_{2}(t){r}^{2} + {V }_{1}(t)r + {V }_{0}(t)\}$, where V ₀, V ₁ and V ₂ are 2π-periodic. The monodromy, for an ordinary differential equation with periodic coefficients, expresses the “rotation” of the general solution over a period.