A power series analysis of bound and resonance states of one-dimensional Schrödinger operators with finite point interactions
作者：
Highlights：
• 1D Schrödinger operators with interactions are described by suitable extensions.
• Point interactions lead to matrix interaction conditions at discrete points.
• Characteristic equations of resonance and bound states share similar structures.
• Resonance and bound states admit a similar spectral analysis.
• Exact expressions for eigenstates and resonance states are given as power series.
• Numerical analysis of bound and resonance states reduces to finding polynomial roots.
摘要
•1D Schrödinger operators with interactions are described by suitable extensions.•Point interactions lead to matrix interaction conditions at discrete points.•Characteristic equations of resonance and bound states share similar structures.•Resonance and bound states admit a similar spectral analysis.•Exact expressions for eigenstates and resonance states are given as power series.•Numerical analysis of bound and resonance states reduces to finding polynomial roots.
论文关键词：Point interactions,One-dimensional Schrödinger operators,Bound states,Resonance states,Spectral parameter power series
论文评审过程：Received 14 June 2020, Revised 30 September 2021, Accepted 2 November 2021, Available online 16 November 2021, Version of Record 16 November 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126774
