Generalized Boundary Conditions for the qBounce Experiment

• URL: http://arxiv.org/abs/2510.15341v1
• Date: Fri, 17 Oct 2025 06:11:38 GMT
• Title: Generalized Boundary Conditions for the qBounce Experiment
• Authors: Eric J. Sung, Benjamin Koch, Tobias Jenke, Hartmut Abele, Denys I. Bondar,
• Abstract summary: We show how boundary conditions are implemented for ultracold neutrons bouncing above a mirror in Earth's gravity.<n>Our results emphasize that enforcing self-adjointness-and modeling the correct boundary physics-is essential for quantitative predictions in gravitational quantum states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Discrepancies between theory and recent qBounce data have prompted renewed scrutiny of how boundary conditions are implemented for ultracold neutrons bouncing above a mirror in Earth's gravity. We apply the theory of self-adjoint extensions to the linear gravitational potential on the half-line and derive the most general boundary condition that renders the Hamiltonian self-adjoint. This introduces a single real self-adjoint parameter $\lambda$ that continuously interpolates between the Dirichlet case and more general (Robin-type) reflecting surfaces. Building on this framework, we provide analytical expressions for the energy spectrum, eigenfunctions, relevant matrix elements, and a set of sum rules valid for arbitrary $\lambda$. We show how nontrivial boundary conditions can bias measurements of $g$ and can mimic or mask putative short-range ''fifth-force''. Our results emphasize that enforcing self-adjointness-and modeling the correct boundary physics-is essential for quantitative predictions in gravitational quantum states. Beyond neutron quantum bounces, the approach is broadly applicable to systems where boundaries and self-adjointness govern the observable spectra and dynamics.

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