Formal and Precise Derivation of the Green Functions for a Simple Potential
R. de la Madrid
Abstract
In formal scattering theory, Green functions are obtained as solutions of a distributional equation. In this paper, we use the Sturm-Liouville theory to compute Green functions within a rigorous mathematical theory. We shall show that both the Sturm-Liouville theory and the formal treatment yield the same Green functions. We shall also show how the analyticity of the Green functions as functions of the energy keeps track of the so-called ``incoming'' and ``outgoing'' boundary conditions.
Create a lesson
Related papers
Parallel quantum channel discrimination and numerical ranges in tensor product subspaces
Adam Bílek, Paulina Lewandowska, Ryszard Kukulski
Asymptotically Good Quantum Locally Testable Codes
William Gay, Fernando Granha Jeronimo
All causally separable quantum processes are quantum circuits with classical control of causal order
Julian Wechs, Alastair A. Abbott, Cyril Branciard
Analytic leakage suppression with a single control field: fast two-qubit gates with tunable couplers
Lukas Heunisch, Michael J. Hartmann, Aashish A. Clerk
Procrastinating einselection in non-Markovian quantum dynamics
Michael J. Moody, Tara Kalsi, Agung Budiyono et al.
Quantum Entropy Contraction and Factorization from Hypercontractivity
Li Gao, Lijun Wang