Intensive Course: Guaranteed Computation of Schrödinger Eigenvalue Problems

Speaker: Xuefeng LIU (Tokyo Woman's Christian University)

Time: 10:30-12:00, July 28^th, Tuesday

16:30-18:00, July 28^th, Tuesday

09:00-10:30, July 30^th, Thursday

14:30-16:00, July 30^th, Thursday

Venue: 5107, the 5^th Teaching Building

Contents:

1. Introduction to Eigenvalue Problems and the Min–Max / Max–Min Principles

* Ritz upper bounds for eigenvalues

* The finite element method (FEM)

* Spectral methods

2. Projection-Based Lower Bounds for the Laplacian Eigenvalue Problem

* Lower bounds using conforming FEM

* Lower bounds using nonconforming FEM

* Lower bounds using spectral methods

3. The Kato–Lehmann–Goerisch Method for High-Precision Lower Eigenvalue Bounds

* Kato’s method

* Lehmann’s method

* Goerisch’s technique

4. Guaranteed Bounds for Schrödinger Eigenvalue Problems on \mathbb{R}^n

* Finite computational domains for infinite-domain problems

* Dirichlet and Neumann boundary conditions

* Confining potentials

* Coulomb potentials