# The maximal 'kinematical' invariance group for an arbitrary potential revised

## TL;DR

This paper revises the classification of symmetries in Schrödinger equations with arbitrary potentials, providing a corrected list of potentials and their symmetry groups, along with precise algebraic identifications.

## Contribution

It offers a corrected and complete classification of potential functions and their symmetry groups for Schrödinger equations, improving upon previous work.

## Key findings

- Corrected list of non-equivalent potentials
- Exact identification of symmetry algebras
- Admissible equivalence transformations established

## Abstract

Group classification of one particle Schr\"odinger equations with arbitrary potentials (C. P. Boyer, Helv. Phys. Acta {\bf 47}, p. 450, 1974) is revised. The corrected completed list of non-equivalent potentials and the corresponding symmetries is presented together with exact identification of symmetry algebras and admissible equivalence transformations.