5 problems

Exit statistics theorem. Neglecting the possibility of clustering, the flux-across-surfaces theorem for potential scattering should generalize to this $N$-particle setting: for eve…

Let $\Gamma$ be a smooth curve that is a local deformation of a straight line, with curvature $\kappa$, and let $\alpha$ be the coupling strength in the leaky-wire Hamiltonian. Def…

The scattering problem concerns finite, truncated potentials with reflectionless above-barrier states that propagate as plane waves at infinity. The corresponding unbounded potenti…

Let $R_{left}(k)$ and $R_{right}(k)$ denote the reflection probabilities for incidence from the left and right, respectively, and let $T(k)$ denote the transmission probability at…

Conjecture 1. Any discontinuities in the scattering potential cause a series of extra resonance poles below and along the real $k$ axis as well as along the real $E$ axis.