𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the bound state of Schrödinger operators in one dimension

✍ Scribed by M. Klaus

Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
723 KB
Volume
108
Category
Article
ISSN
0003-4916

No coin nor oath required. For personal study only.

✦ Synopsis

Under certain conditions on the potential a one-dimensional Schradinger operator has a unique bound state in the limit of weak coupling while under other conditions no bound state is present in this limit. This question is investigated for potentials obeying s (1 + ] x I) I V(x)1 dx < ~0. An asymptotic formula for the bound state is proven.

📜 SIMILAR VOLUMES

The bound state of weakly coupled Schröd
The bound state of weakly coupled Schrödinger operators in one and two dimensions
✍ Barry Simon 📂 Article 📅 1976 🏛 Elsevier Science 🌐 English ⚖ 443 KB

We study the unique bound state which (-d2/dx2) + hV and -A + XV (in two dimensions) have when A is small and V is suitable. Our main results give necessary and sufficient conditions for there to be a bound state when h is small and we prove analyticity (resp. nonanalyticity) of the energy eigenvalu

On Positive Solutions of Critical Schröd
On Positive Solutions of Critical Schrödinger Operators in Two Dimensions
✍ F. Gesztesy; Z. Zhao 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 696 KB

Using a probabilistic approach based on the Feynman-Kac formalism and the spectral radius of the shuttle operator, we prove that two-dimensional Schrödinger operators \(H=-\Delta+V\) with short-range potentials \(V\) satisfying \(V(x)=\left.\right|_{\mid x \rightarrow \infty} 0\left(|x|^{-2}(\ln (|x