Many-Body-Systems and Exciton Model in New-Tamm-Dancoff- Formulation
F. Wahl · Zeitschrift für Naturforschung A · 1975
The NTD-method is a procedure to compute differences of eigenvalues in quantum mechanical problems: ωαβ=λα-λβ. It is an instruction to transform and truncate an infinite linear system of eigenvalue equations ω τk= Ak m τm which is derived with the aid of fundamental field equations or corresponding Hamilton-operators, as e.g. with Heisenberg's nonlinear spinor equation. In this paper we want to test the NTD-method for a many-body-model in solid state physics. We elaborate on the physical and mathematical aspects by choosing a suitable transformation τ → φ = C τ to get a new linear 1 system ω φk= Bkk+2iφk+2i which permits a truncation to evaluate approximation of states. The efficiency of this method is demonstrated by treating a two-body-system in presence of polarisation quanta, known as exciton model