Bound states of two-dimensional Schrödinger-Newton equations

2008/07/25 by Joachim Stubbe, Stubbe, Joachim · 1 citation
Mathematics · #Spectral Theory in Mathematical Physics #advanced mathematical theories #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.0807.4059

Abstract

We prove an existence and uniqueness result for ground states and for purely angular excitations of two-dimensional Schrödinger-Newton equations. From the minimization problem for ground states we obtain a sharp version of a logarithmic Hardy-Littlewood-Sobolev type inequality.

Citations

• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• On Gravity's role in Quantum State Reduction

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• On planar Schrodinger-Poisson systems with repulsive interactions in the mass supercritical regime

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