Potential scatterings in $L^2$ space: (1) non-orthogonality of stationary states

Kenzo Ishikawa

Published 2023-05-26Version 1

Orthogonality of eigenstates of different energies held in bound states plays important roles, but is dubious in scattering states. Scalar products of stationary scattering states are analyzed using solvable models, and an orthogonality is shown violated in majority potentials. Consequently their superposition has time dependent norm and is not suitable for a physical state. Various exceptional cases are clarified. From the results of the first paper,a perturbative and variational methods emerge as viable methods for finding a transition probability of normalized initial and final states.