Manuscript Em03-F@1 · Em03-F-v1.tex · section · 0d4d148b

Outgoing scalar packet identification and normality

Outgoing scalar packet identification and normality · lines 833–862

Em03-F@1#eq:outcoefficient

For a normalized compact-band packet $h$ , stationary scattering gives

b_{h} = a_{out} (h) = a (v_{h}), v_{h} = (τ h, ρ_{I} h) .

Thus

∥ v_{h} ∥_{0} = 1, Q_{h} = X (v_{h}) / 2, P_{h} = X (i v_{h}) / 2 .

Define the outgoing source coefficient

d_{\infty} (ω) = τ (ω) k_{F, H} (ω) + ρ_{I} (ω) k_{F, I} (ω), c_{h} = ⟨ v_{h}, k_{F} ⟩ = \int h d_{\infty} d ω .

If $S (ω)$ is the complete scattering matrix, the other component of $S k_{F}$ is denoted $d_{hor}$ .

Displayed formulas in this passage

Em03-F@1#eq:outcoefficient · line 850
$d_{\infty} (ω) = τ (ω) k_{F, H} (ω) + ρ_{I} (ω) k_{F, I} (ω), c_{h} = ⟨ v_{h}, k_{F} ⟩ = \int h d_{\infty} d ω .$
unlabeled · line 838
$b_{h} = a_{out} (h) = a (v_{h}), v_{h} = (τ h, ρ_{I} h) .$
unlabeled · line 843
$∥ v_{h} ∥_{0} = 1, Q_{h} = X (v_{h}) / 2, P_{h} = X (i v_{h}) / 2 .$