Mathematical theory of the Wigner-Weisskopf atom

Abstract

In these lectures we shall study an "atom", S, described by finitely many energy levels, coupled to a "radiation field", R, described by another set (typically continuum) of energy levels. More precisely, assume that S and R are described, respectively, by the Hilbert spaces hS, hR and the Hamiltonians hS, hR. Let h = hS ⊕ hR and h0 = hS ⊕ hR. If v is a self-adjoint operator on h describing the coupling between S and R, then the Hamiltonian we shall study is hλ ≡ h0 + λv, where λ ∈ ℝ is a coupling constant. © 2006 Springer.