A Solvable Model of a Nonlinear extension of Quantum Mechanics

TL;DR

This paper presents an exactly solvable nonlinear extension of quantum mechanics, aiming to clarify interpretational issues related to measurement by leveraging the eigenstructure of the linear theory.

Contribution

It introduces a specific nonlinear quantum model that remains exactly solvable using linear quantum eigenvalues and eigenfunctions, providing a new tool for understanding measurement.

Findings

The nonlinear model is exactly solvable using linear eigenvalues and eigenfunctions.

It offers insights into the interpretation of nonlinear quantum theories.

The model helps address questions about quantum measurement theory.

Abstract

We introduce 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. We hope that this simple example will elucidate some of the issues of interpreting nonlinear generalization of quantum mechanics that have been put forth to resolve questions about quantum measurement theory.