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September 10, 2025Journal of Physics A Mathematical and Theoretical17 citations

Transparent boundary conditions for the stationary Schrödinger equation via Weyl-Titchmarsh theory

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VDVolodymyr DerkachCTCarsten TrunkJYJambul Yusupov

Key Points

  • Transparent boundary conditions can be formulated using Weyl-Titchmarsh coefficients for various potentials.
  • The methods were illustrated using the harmonic potential and the Pöschl-Teller potential as specific cases.
  • This general approach expands the techniques used to address boundary conditions in quantum mechanics.
  • The findings have potential implications for quantum systems modeled by the stationary Schrödinger equation.

Abstract

Abstract We propose a general approach for deriving transparent boundary conditions for the stationary Schrödinger equation with arbitrary potential. It is proven that the transparent boundary conditions can be written in terms of the Weyl-Titchmarsh coefficients. As examples for the application of the proposed approach, two special cases for the stationary Schrödinger equation with the harmonic potential and the Pöschl-Teller potential are considered.

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Cite This Study

Derkach et al. (2025) studied this question.

synapsesocial.com/papers/68c1b18b54b1d3bfb60e88d2https://doi.org/10.1088/1751-8121/adf787
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Discrete Transparent Boundary Conditions for Wide Angle Parabolic Equations in Underwater Acoustics1998 · 87 citations
  2. 2THE ASYMPTOTIC FORM OF THE TITCHMARSH-WEYL m -FUNCTION1984 · 25 citations
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  4. 4A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in ( 1 + 1 ) D2013 · 56 citations
  5. 5Absorbing boundary conditions for nonlinear Schrödinger equations2006 · 50 citations