Geometric Interpretation of a nonlinear extension of Quantum Mechanics

TL;DR

This paper explores a nonlinear extension of quantum mechanics, interpreting wave function components as different spacetime regions and linking nonlinearities to gravitational effects, with exact solvability based on linear quantum eigenvalues.

Contribution

It introduces a solvable nonlinear quantum framework where wave components relate to spacetime regions and gravitational effects emerge from nonlinear terms.

Findings

Nonlinear quantum mechanics can be exactly solved using linear eigenvalues.

Wave function components correspond to different asymptotic spacetime regions.

Nonlinear terms may be interpreted as gravitational effects.

Abstract

We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. In this paper we suggest that the two components of the wave function represent the system described by the Hamiltonian H in two different asymptotic regions of spacetime and we show that the non-linear terms can be viewed as giving rise to gravitational effects.