The one-dimensional Schr\"{o}dinger-Newton equations
Ph. Choquard, J. Stubbe
TL;DR
This paper establishes the existence and uniqueness of ground state solutions for the one-dimensional Schrödinger-Newton equations, contributing to the mathematical understanding of this nonlinear quantum-gravity system.
Contribution
It provides the first rigorous proof of existence and uniqueness of ground states for the one-dimensional Schrödinger-Newton equations.
Findings
Proved existence of ground states
Demonstrated uniqueness of solutions
Enhanced understanding of nonlinear quantum-gravity models
Abstract
We prove an existence and uniqueness result for ground states of one-dimensional Schr\"{o}dinger-Newton equations.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Stability and Controllability of Differential Equations · Numerical methods in inverse problems