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<p>In this paper, we study the existence of a bound state solution for the stationary Schrödinger equation, which includes both a magnetic potential and an electric potential. Under certain assumption about the exponential decay of the combined magnetic and electric potentials, the existence of a least energy solution is established. Additionally, we provide a weaker sufficient condition for the existence of a bound state solution. Our approach is mainly based on the variational method.</p>

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On bound states of Schrödinger equation with vanishing magnetic potential

  • 期刊论文

  • 发表日期：

    2025年5月5日

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  • Baihong Li,
  • Yuanhong Wei

摘要

In this paper, we study the existence of a bound state solution for the stationary Schrödinger equation, which includes both a magnetic potential and an electric potential. Under certain assumption about the exponential decay of the combined magnetic and electric potentials, the existence of a least energy solution is established. Additionally, we provide a weaker sufficient condition for the existence of a bound state solution. Our approach is mainly based on the variational method.