Schrodinger Equations for Higher Order Non-relativistic Particles and N-Galilean Conformal Symmetry

TL;DR

This paper explores higher-order Schrödinger equations for non-relativistic particles and demonstrates their invariance under extended Galilean conformal symmetries in various dimensions.

Contribution

It introduces higher-derivative Schrödinger equations and analyzes their invariance under N-Galilean conformal algebras, extending symmetry understanding in non-relativistic quantum mechanics.

Findings

Higher-order Schrödinger equations are invariant under N(odd)-extended Galilean conformal algebras.

In 2+1 dimensions, the equations are invariant under N(even)-GCA.

The work broadens the symmetry framework for non-relativistic quantum systems.

Abstract

We consider Schrodinger equations for a non-relativistic particle obeying N+1-th order higher derivative classical equation of motion. These equations are invariant under N(odd)-extended Galilean conformal (NGC) algebras in general d+1 dimensions. In 2+1 dimensions, the exotic Schrodinger equations are invariant under N(even)-GCA.