On quantum mechanics as constrained N=2 supersymmetric classical mechanics

TL;DR

This paper demonstrates that the Schrödinger equation can be reformulated as a constrained Liouville equation within an extended Grassmann phase space, revealing an underlying N=2 supersymmetry in one-dimensional systems.

Contribution

It introduces a novel formulation linking quantum mechanics to classical supersymmetric mechanics through Grassmann algebra extensions.

Findings

Schrödinger equation equivalent to constrained Liouville equation

Underlying N=2 supersymmetry in one-dimensional systems

Potential for applying this framework to realistic theories

Abstract

The Schr\"odinger equation is shown to be equivalent to a constrained Liouville equation under the assumption that phase space is extended to Grassmann algebra valued variables. For onedimensional systems, the underlying Hamiltonian dynamics has a N=2 supersymmetry. Potential applications to more realistic theories are briefly discussed.