Essential Self-Adjointness of Semi-Bounded Schrödinger Operators on Birth-Death Chains
Abstract
We study the essential self-adjointness of semi-bounded Schrödinger operators on birth-death chains. First, we offer a general characterization which originates from studying a second order linear recurrence with variational coefficients which comes from the Schrödinger. As this characterization is algebraically complicated, we present an additional theorem discussing the failure of essential self-adjointness. Finally, we study two specific cases of solutions to equations involving the Schrödinger operator over birth-death chains and derive explicit formulas in these cases.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
advanced mathematical theories
Algebraic and Geometric Analysis
Publication details
- Journal / source
- The PUMP Journal of Undergraduate Research
- Volume
- 9
- Pages
- 275–290
- Publication date
- 14 July 2026
- Language
- EN