Two-particle bound states at interfaces and corners

We study two interacting quantum particles forming a bound state in $d$-dimensional free space, and constrain the $k$ directions to $(0,\infty)^k \times \mathbb{R}^{d-k}$, with Neumann boundary conditions. First, we prove that ground energy strictly decreases upon going from $k+1$. This shows stick corner where all planes intersect. Second, show for resulting Hamiltonian, after removing part of kinetic energy, has only finitely many eigenvalues below essential spectrum. paper generalizes work Egger, Kerner Pankrashkin (J. Spectr. Theory 10(4):1413--1444, 2020) dimensions $d>1$.