Absence of reflection as a function of the coupling constant
| dc.creator | Killip, Rowan | |
| dc.creator | Sims, Robert | |
| dc.date | 2006-01-17 | |
| dc.date | 2006-05-03 | |
| dc.date.accessioned | 2026-07-07T06:58:23Z | |
| dc.date.available | 2026-07-07T06:58:23Z | |
| dc.description | We consider solutions of the one-dimensional equation $-u'' +(Q+ λV) u = 0$ where $Q: \mathbb{R} \to \mathbb{R}$ is locally integrable, $V : \mathbb{R} \to \mathbb{R}$ is integrable with supp$(V) \subset [0,1]$, and $λ\in \mathbb{R}$ is a coupling constant. Given a family of solutions $\{u_λ \}_{λ\in \mathbb{R}}$ which satisfy $u_λ(x) = u_0(x)$ for all $x<0$, we prove that the zeros of $b(λ) := W[u_0, u_λ]$, the Wronskian of $u_0$ and $u_λ$, form a discrete set unless $V \equiv 0$. Setting $Q(x) := -E$, one sees that a particular consequence of this result may be stated as: if the fixed energy scattering experiment $-u'' + λV u = Eu$ gives rise to a reflection coefficient which vanishes on a set of couplings with an accumulation point, then $V \equiv 0$. | |
| dc.description | To appear in Journal of Mathematical Physics | |
| dc.identifier | https://arxiv.org/abs/math-ph/0601033 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0601033 | |
| dc.identifier | J. Math. Phys. 47, 062102 (2006) | |
| dc.identifier | doi:10.1063/1.2206691 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107339 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 47A40; 34L25 | |
| dc.title | Absence of reflection as a function of the coupling constant | |
| dc.type | text |