具有二次增长限制势的Schrödinger算子

IF 1.6 3区数学 Q1 MATHEMATICS

Analysis and Mathematical Physics Pub Date : 2025-05-27 DOI:10.1007/s13324-025-01063-9

Chiara Alessi, Lorenzo Brasco, Michele Miranda

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引用次数: 0

摘要

我们研究了Schrödinger算子在限定势下的谱性质，限定势由到固定紧致势阱的距离平方给出。我们证明了本征值和本征态的连续性估计、基态能量的下界、本征态的正则性和可积性。我们还利用初等非线性方法得到了在无穷远处的显式衰减估计。

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A Schrödinger operator with confining potential having quadratic growth

We study the spectral properties of a Schrödinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove continuity estimates on both the eigenvalues and the eigenstates, lower bounds on the ground state energy, regularity and integrability properties of eigenstates. We also get explicit decay estimates at infinity, by means of elementary nonlinear methods.

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来源期刊

Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

0.00%

发文量

122

期刊介绍： Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.