# Scattering theory for repulsive Schr\"odinger operators and applications to limit circle problem

## TL;DR

This paper investigates the resolvent existence for repulsive Schrödinger operators, especially those not essentially self-adjoint on Schwartz space, and revisits classical results on their self-adjointness with large repulsive constants.

## Contribution

It extends the understanding of resolvent existence for non-self-adjoint repulsive Schrödinger operators and revisits classical self-adjointness results.

## Key findings

- Existence of outgoing/incoming resolvents for certain repulsive Schrödinger operators
- Large repulsive constants lead to non-essential self-adjointness
- Reconfirmation of classical self-adjointness results

## Abstract

In this note, we study existence of the outgoing/incoming resolvents of repulsive Schr\"odinger operators which may not be essentially self-adjoint on the Schwartz space. Moreover, we recover the classical result: The repulsive Schro\"odinger operators with large repulsive constant is not essentially self-adjoint on the Schwartz space.