Isometric Entanglement of Particle Positions in Quantum Bound Systems

TL;DR

This paper demonstrates that the scalar potential in the Schrödinger equation for two-particle systems can be interpreted as an isometric entanglement of their position coordinates, transforming the equation into a potential-free form.

Contribution

It introduces a novel perspective linking scalar potentials to entangled position coordinates, providing a new way to analyze quantum bound systems.

Findings

Scalar potential corresponds to isometric entanglement of particle positions.

Transforming to entangled coordinates removes the scalar potential from the Schrödinger equation.

Entangled coordinates are complex and relate through an entangling transformation to real positions.

Abstract

It is shown the role of a scalar potential in the Schr\"{o}dinger equation for a steady-state two-particle system is equivalent to an isometric entanglement of the position coordinates of the particles in space and time. The entangled coordinates of each particle are complex quantities related through the entangling transformation to the real positions of both particles. The transformation takes into account all of the states in the Hilbert space of the composite system. Transforming the Schr\"{o}dinger equation into these entangled coordinates eliminates the scalar potential.