Wave Equations with Point Interactions in Finite Energy Space

Details Wave Equations with Point Interactions in Finite Energy Space Wave Equations with Point Interactions in Finite Energy Space

2000-10-27

arxiv.org/abs/math-ph/0010047v2

Physics

Mathematical Physics

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

Scientific paper

Given the abstract wave equation $\ddot\phi-\Delta_\alpha\phi=0$, 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

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