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August 19, 2026AtomsOpen Access

Transformation Between Regular-Irregular Schrödinger Equation Solution Pairs by Means of the Corresponding Milne Function Properties

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Authors

SDS. DanakasSCS. Cohen

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Overview

Theoretical study demonstrates transformation between Schrödinger equation solution pairs using Milne functions, indicating the regular solution unifies differing boundary conventions.

Key Points

  • To establish a mathematical framework using the Milne transformation for converting regular and irregular Schrödinger equation solution pairs between different asymptotic phase and amplitude conventions.
  • Applied the Milne transformation (Phase-Amplitude Method) to one-particle radial Schrödinger equations.
  • Evaluated the switching formalism across two model potentials: a repulsive Coulomb barrier and a Coulomb-Stark potential modeling hydrogen in a static homogeneous electric field.
  • Formulated a rigorous mathematical framework that enables exact switching between standard and reversed asymptotic phase representations.
  • Demonstrated that the regular solution serves as the unifying thread linking different irregular solution representations across scattering and tunneling domains.

Cite This Study

Danakas et al. (2026) studied this question.

synapsesocial.com/papers/6a8563c403308d306e2d71d1https://doi.org/10.3390/atoms14080071
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