Year: 2014
Type: preprint
Abstract: The Dirichlet problem on a bounded planar domain is more readily understood and solved for the Laplace operator than it is for a Schrodinger operator. When the potential function is small, we might hope to approximate the solution to the Schrodinger equation with the solution to the Laplace equation. In this vein we develop a series expansion for the solution and give explicit bounds on the error terms when truncating the series. We also examine a handful of examples and derive similar results for the Green function and Dirichlet-to-Neumann map.
Source: arXiv (Cornell University)
Author: Martin, Charles Z.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2188756735