Wave Equations with Point Interactions in Finite Energy Space

Abstract

Given the abstract wave equation $\ddot{\varphi }-{\Delta }_{\alpha }\varphi =0$, where ${\Delta }_{\alpha }$ is the Laplace operator with a point interaction of strength $\alpha$, we define and study ${\bar{W}}_{\alpha }$, the associated wave generator in the phase space of finite energy states. We prove the existence of the phase flow generated by ${\bar{W}}_{\alpha }$, and describe its most relevant properties with particular emphasis on the associated symplectic structure and scattering theory

misprints corrected. 26 pages. To appear in J. Math. Phys

References in corpus (2)

• Schrodinger Equation with Moving Point Interactions in Three Dimensions
• Delta Interactions and Electrodynamics of Point Particles

Cited by in corpus (1)

• Wave equation with concentrated nonlinearities