Positivity of the two-dimensional Brown—Ravenhall operator

DOI10.1017/S0308210510001708zbMATH Open1256.81039arXiv1010.6300OpenAlexW2962849365MaRDI QIDQ3165521

Stefan Walter

Publication date: 29 October 2012

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Abstract: We determine the critical coupling of the two-dimensional Brown-Ravenhall operator with Coulomb potential. Boundedness from below has essentially been proven by Bouzouina, whose work however contains a trivial error leading to a wrong constant exactly one half of the actual critical constant. Furthermore we show that the operator is in fact positive. Our proof of that is for the most part analogous to Tix's proof of the corresponding result for the three-dimensional operator.

Full work available at URL: https://arxiv.org/abs/1010.6300

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Schrödinger operator, Schrödinger equation (35J10)

Related Items (1)

On the stability and spectral properties of the two-dimensional Brown-Ravenhall operator with a short-range potential

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