Year: 2026
Type: preprint
Abstract: For every $d\ge2$ and $0\leσ<1/3$, we construct with LLM-assistance a smooth bounded nonnegative lens-type potential $V$ with arbitrarily small $\|V\|_\infty+\int_{\mathbb{R}^d}|x|^{1-d+σ}|V(x)|^2 dx$, such that $-Δ+V$ has only pure point spectrum in $(0,\infty)$. Thus, we show that Barry Simon's $L^2$ conjecture, Problem 8 in "Schrödinger operators in the twenty-first century", is false.
Source: arXiv (Cornell University)
Authors: Becker, Simon, Yang, Mengxuan
Institutions: Bocconi University, Texas A&M University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223390522