Manuscript Em03-A@1 · Em03-A-v1.tex · section · 6d54627d

The main emission theorem

The main emission theorem · lines 272–294

Em03-A@1#eq:packet

For a compact frequency interval

B = [ω_{-}, ω_{+}] \subset (0, \infty),

let $h \in C^{\infty}_{c} ((0, \infty))$ satisfy

supp h \subset B, \int_{0}^{\infty} ∣ h (ω) ∣^{2} d ω = 1.

Define the outgoing packet annihilator and number observable by

a_{out} (h) = \int_{0}^{\infty} h (ω) a_{out} (ω) d ω, N_{h} = a_{out} (h)^{*} a_{out} (h) .

Their construction and finite expectation are proved below.

Displayed formulas in this passage

Em03-A@1#eq:packet · line 285
$a_{out} (h) = \int_{0}^{\infty} h (ω) a_{out} (ω) d ω, N_{h} = a_{out} (h)^{*} a_{out} (h) .$
unlabeled · line 275
$B = [ω_{-}, ω_{+}] \subset (0, \infty),$
unlabeled · line 279
$supp h \subset B, \int_{0}^{\infty} ∣ h (ω) ∣^{2} d ω = 1.$