Bounds states of the Schrödinger-Newton model in low dimensions

doi:https://doi.org/10.48550/arxiv.0812.2152

Open AccessPreprint10.48550/arxiv.0812.2152

Bounds states of the Schrödinger-Newton model in low dimensions

Joachim Stubbe,Marc Vuffray-2008-12-11-ArXiv.org

TL;DRAbstract

We prove the existence of quasi-stationary symmetric solutions with exactly n>=0 zeros and uniqueness for n=0 for the Schrödinger-Newton model in one dimension and in two dimensions along with an angular momentum m>=0. Our result is based on an analysis of the corresponding system of second-order differential equations.

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We prove the existence of quasi-stationary symmetric solutions with exactly n>=0 zeros and uniqueness for n=0 for the Schrödinger-Newton model in one dimension and in two dimensions along with an angular momentum m>=0. Our result is based on an analysis of the corresponding system of second-order differential equations.

Keywords

Uniqueness Dimension (graph theory)Order (exchange)Mathematics Angular momentum Schrödinger's cat Mathematical physics Momentum (technical analysis)

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