Gauge- and coordinate-invariant equations for two-component systems

TL;DR

This paper derives gauge- and coordinate-invariant Schrödinger-like equations for two-component systems, providing a robust framework for analyzing molecular wavefunctions with exact factorization.

Contribution

It introduces gauge- and coordinate-invariant formulations of equations for two-component systems, enhancing the theoretical foundation of molecular quantum mechanics.

Findings

Derived invariant equations for marginal and conditional amplitudes.

Presented coupled equations equivalent to molecular Schrödinger equation.

Demonstrated the approach with a nonrelativistic molecular example.

Abstract

The Schr\"odinger-like equations for the marginal and conditional probability amplitudes resulting from the exact factorization of the wavefunction of a two-component system are derived in a form that is invariant to gauge and coordinate transformations. Coupled equations equivalent to the nonrelativistic Schr\"odinger equation of a molecule are derived as an example.