Песочница1

[math]\frac{e^{ik | x - x_{0}|}}{4 \pi | x - x_{0}|}[/math] [math]D(H^{*}_{0}) = v_{0} + a^{+} G(x, x_{0}, k^2_0) + a^{-} G(x, x_{0}, \overline{k^2_0})[/math] [math]- \Delta {}_{0}[/math] [math]- \Delta {}^{*}_{0}[/math] [math]D(H^{*}_{0}) = v_{0} + a_{v} \cdot \frac{e^{i k |x-x_0|}}{4 \pi |x-x_0|}[/math] [math](- \Delta u, v) - (u, \Delta v)[/math] [math](- \Delta u, v) - (u, \Delta v) = \int\limits_{\delta (R^3 \backslash B_{\epsilon})} (- \frac{\delta u}{\delta n} \bar v + \frac{\delta \bar v}{\delta n} u) ds[/math] [math]a_{u} = \alpha \cdot u_{0}(0), Im \alpha = 0[/math] [math]c_j=e^{i \theta j a} \cdot c_0[/math] [math]d_j=e^{i \theta j a} \cdot d_0[/math] [math]- \Delta \Psi = k^2 \Psi[/math] [math]e^{ik(x, \nu)}[/math] [math]D(H^{*}_{0}) = v_{0} + \sum\limits_{j} c_{j} \cdot \frac{e^{i k |x-x_0|}}{4 \pi |x-x_0|} + \sum\limits_{j} d_{j} \cdot \frac{e^{i k |x-x_0|}}{4 \pi |x-x_0|}[/math]