刘雪峰 教授（东京女子大学）

周爱辉 研究员

Rigorous Two-Sided Eigenvalue Bounds for Schrödinger Operators on ℝ²

5月14日（周四）10:00-11:00，南楼402

We propose a rigorous method for computing two-sided eigenvalue bounds of the Schrödinger operator

H = -Δ + V

on ℝ² with a given potential V.

The method combines domain truncation to a disk D(R) with the Composite Enriched Crouzeix–Raviart (CECR) finite element method. A key ingredient is Liu’s eigenvalue bound theorem for nonconforming finite elements, which enables the derivation of guaranteed bounds.

Two representative potentials are investigated: the radially symmetric ring potential

V₁(x) = (|x|² - 1)², and the Cartesian double-well potential

V₂(x) = (x₁² - 1)² + x₂².