# Rellich's theorem for spherically symmetric repulsive Hamiltonians

## TL;DR

This paper proves Rellich's theorem for spherically symmetric repulsive Hamiltonians, identifying the maximal weighted space where eigenfunctions are absent using a novel, elementary commutator method based on radial flow conjugation.

## Contribution

Introduces a simple, elementary proof of Rellich's theorem for specific Hamiltonians using a new conjugate operator linked to radial flow, avoiding advanced analytical tools.

## Key findings

- Established the largest weighted space with no eigenfunctions for the Hamiltonians.
- Developed a new commutator-based proof technique using radial flow conjugation.
- Simplified the proof of Rellich's theorem without advanced tools.

## Abstract

For spherically symmetric repulsive Hamiltonians we prove Rellich's theorem, or identify the largest weighted space of Agmon-H\"ormander type where the generalized eigenfunctions are absent. The proof is intensively dependent on commutator arguments. Our novelty here is a use of conjugate operator associated with some radial flow, not with dilations and translations. Our method is simple and elementary, and does not employ any advanced tools such as the operational calculus or the Fourier analysis.