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arXiv · 2305.16939

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

Kenzo Ishikawa
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Abstract

Orthogonality of eigenstates of different energies and its implications in potential scattering are unlabeled. Scalar products of scattering states of different energies are found to have finite non-orthogonal terms in potentials of finite widths. Their superpositions have time-dependent norms, and are not suitable for isolate states. In these systems, a perturbative method and a variational method are viable methods for finding a rigorous transition probability that describes phenomena completely. In various exceptional potentials, an orthogonality is satisfied.

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Kenzo Ishikawa. 2023-05-26. Potential scatterings in $L^2$ space: (1) non-orthogonality of stationary states. https://arxiv.org/abs/2305.16939

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