Lung-Hui Chen

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Articles: 1

Reconstruction of Piecewise Constant Potential with Phaseless Reflection Coefficient

MFAT 32 (2026), no. 2, 116-128

116-128

Let us consider the scattering theory of one-dimensional Schrödinger equation defined by piecewise constant potentials with compact support. We construct the asymptotics of reflection coefficient by iterating the transition matrices. The jump points of the step potential appear in the asymptotics of reflection coefficient. Accordingly, we investigate the modulus of reflection coefficient. The modulus is connected to the zero set of reflection coefficient via Nevanlinna-Levin type of representation theorem. The growth theory of zero set of the reflection coefficient plays a role.

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