Spin-Momentum Impedance and Filtering by a Spin-Coupled Absorbing Boundary Condition

Absorbing boundaries are often treated as scalar sinks. Here we show that a spin-coupled absorbing boundary for a Pauli particle acts instead as a spin–momentum impedance. Its tangential boundary symbol has two branches, $i\kappa \pm \mathrm{\mid }\mathit{\xi }\mathrm{\mid }$, coupling normal absorption to in-plane momentum. In a harmonic guide, the transverse ground state samples $\mathrm{\mid }\mathit{\xi }\mathrm{\mid }\sim {\mathrm{\ell }}_{\perp }^{-1}\sim \sqrt{\omega }$; narrowing the guide therefore strengthens a local evanescent boundary response without introducing a bulk potential barrier. Solving the detector-present spinor absorbing-boundary evolution, we identify boundary-induced filtering: the prompt detector flux is suppressed, the fixed-window detected fraction is reduced, and a delayed oscillatory sector appears. Over that window the restricted mean detection time is fitted by $A+B\sqrt{\omega }$, with setup-dependent coefficients. The robust result is a spin–momentum filtering mechanism with boundary scale $\mathrm{\mid }\mathit{\xi }\mathrm{\mid }\sim \sqrt{\omega }$, not a universal arrival-time law.