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

• URL: http://arxiv.org/abs/2305.16939v4
• Date: Mon, 1 Jul 2024 01:43:21 GMT
• Title: Potential scatterings in $L^2$ space: (1) non-orthogonality of stationary states
• Authors: Kenzo Ishikawa,
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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