We present a closed-form analytic solution for the propagation of an arbitrary charged scalar state in a nonuniform 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 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 reveals interference-driven dynamics beyond rigid rotation. Our fully relativistic framework provides a practical tool for predicting beam behavior in particle accelerators and electron microscopes.

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• Beam optics
• Dirac equation
• Electron wave interferometry
• Quantum engineering
• Quantum optics
• Quantum state engineering
• Single-particle dynamics
• Angular momentum
• Differential equations
• Electron microscopy
• Geometry
• Nonperturbative methods
• Schroedinger equation