Regensburg 2025 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 29: Poster II

HL 29.57: Poster

Tuesday, March 18, 2025, 18:00–20:00, P1

Quantum Particles on Strongly Bent Curves — •Tim Bergmann, Benjamin Schwager, and Jamal Berakdar — Martin-Luther-Universität Halle-Wittenberg

Quantum systems under geometrical restrictions appear both in research and applied fields such as materials design, for example in the context of quantum wires. In the case of a curve these lead to a one-dimensional Schrödinger equation with its curvature appearing as a potential like term. Up to this point, there existed no ansatz for the treatment of singulary bent curves because the curvature diverges. We provide a solution to this problem for a subclass of such curves, employing a useful mathematical tool for the convergence of eigenvalue equations. This desingularization renders the approximation of the eigenspectrum and corresponding wave functions of systems with singular Hamilton operators possible.

Keywords: Quantum Mechanics on Curves; Strongly Bent Spaces; Singular Hamilton Operators; Eigenspectrum Convergence; Singular Sturm-Liouville Theory