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Orthogonality of eigenstates of different energies and its implications inpotential scattering are unlabeled. Scalar products of scattering states ofdifferent energies are found to have finite non-orthogonal terms in potentialsof finite widths. Their superpositions have time-dependent norms, and are notsuitable for isolate states. In these systems, a perturbative method and avariational method are viable methods for finding a rigorous transitionprobability that describes phenomena completely. In various exceptionalpotentials, an orthogonality is satisfied.

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