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2013•Unpublished venueOpen access

NOTE ON 2D SCHRÖDINGER OPERATORS WITH δ-INTERACTIONS ON ANGLES AND CROSSING LINES

Vladimir Lotoreichik

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Abstract

Abstract. In this note we sharpen the lower bound from [LLP10] on the spectrum of the 2D Schrödinger operator with a δ-interaction supported on a planar angle. Using the same method we obtain the lower bound on the spectrum of the 2D Schrödinger operator with a δ-interaction supported on crossing straight lines. The latter operators arise in the three-body quantum problem with δ-interactions between particles. 1.

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What this paper is about

Abstract. In this note we sharpen the lower bound from [LLP10] on the spectrum of the 2D Schrödinger operator with a δ-interaction supported on a planar angle. Using the same method we obtain the lower bound on the spectrum of the 2D Schrödinger operator with a δ-interaction supported on crossing straight lines. The latter operators arise in the three-body quantum problem with δ-interactions between particles. 1.

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Available abstract

Abstract. In this note we sharpen the lower bound from [LLP10] on the spectrum of the 2D Schrödinger operator with a δ-interaction supported on a planar angle. Using the same method we obtain the lower bound on the spectrum of the 2D Schrödinger operator with a δ-interaction supported on crossing straight lines. The latter operators arise in the three-body quantum problem with δ-interactions between particles. 1.

Key concepts: Schrödinger's cat, Operator (biology), Spectrum (functional analysis), Planar, Bound state, Physics, Essential spectrum, Quantum

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