Manuscript IV@1 · IV.tex · section · 351cb2d7

The numerical self-adjoint generator

Model 1: the fixed vacuum TT plane › The numerical self-adjoint generator · lines 1004–1023

IV@1#eq:A1

H_{1} = L^{2} (R) \otimes Γ_{s} (L^{2} (R^{3})), Q ψ (q) = q ψ (q), Π_{0} ψ (q) = - i \partial_{q} ψ (q),

define initially on the total finite-particle domain

A_{f}^{(1)} (λ) = I \otimes Φ (u_{0, f}) + λ (Q \otimes Φ (u_{e, f}) + Π_{0} \otimes Φ (u_{r, f})) .

The oscillator is identified with a single Fock mode: $Q = (b + b^{†}) / 2$ , $Π_{0} = - i (b - b^{†}) / 2$ .

Displayed formulas in this passage

IV@1#eq:A1 · line 1013
$A_{f}^{(1)} (λ) = I \otimes Φ (u_{0, f}) + λ (Q \otimes Φ (u_{e, f}) + Π_{0} \otimes Φ (u_{r, f})) .$
unlabeled · line 1007
$H_{1} = L^{2} (R) \otimes Γ_{s} (L^{2} (R^{3})), Q ψ (q) = q ψ (q), Π_{0} ψ (q) = - i \partial_{q} ψ (q),$