Universal Analytic Solution for the Quantum Transport of Structured Matter-Waves in Magnetic Optics

• URL: http://arxiv.org/abs/2509.03264v1
• Date: Wed, 03 Sep 2025 12:29:08 GMT
• Title: Universal Analytic Solution for the Quantum Transport of Structured Matter-Waves in Magnetic Optics
• Authors: N. V. Filina, S. S. Baturin,
• Abstract summary: We present a closed-form analytic solution for the propagation of an arbitrary charged scalar state in a non-uniform magnetic field.<n>The dynamics are governed by classical beam optics parameters, the Twiss functions, and phase advance.<n>Our framework provides a powerful tool for predicting beam behavior in particle accelerators and electron microscopes.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a closed-form analytic solution for the propagation of an arbitrary charged scalar state in a non-uniform magnetic field. The dynamics are governed by classical beam optics parameters (Courant-Snyder parameters), the Twiss functions, and phase advance, revealing a direct map between quantum evolution and its classical counterpart. The solution decomposes into three components, exhibiting a complex rotation dependent on the sign of the orbital angular momentum (OAM) projection, alongside an intrinsic distortion from interference governed by a generalized Gouy phase. For a relevant Glaser-type magnetic field and a half-blocked twisted electron, we demonstrate that asymmetry triggers rich dynamics incompatible with a simple Bohmian trajectory interpretation. Our fully relativistic framework provides a powerful tool for predicting beam behavior in particle accelerators and electron microscopes, critical for designing next-generation OAM-based experiments.

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