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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Ishikawa, Kenzo
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910506918346752
author Ishikawa, Kenzo
author_facet Ishikawa, Kenzo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2305_16939
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Potential scatterings in $L^2$ space: (1) non-orthogonality of stationary states
Ishikawa, Kenzo
Quantum Physics
Mathematical Physics
Atomic Physics
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.
title Potential scatterings in $L^2$ space: (1) non-orthogonality of stationary states
topic Quantum Physics
Mathematical Physics
Atomic Physics
url https://arxiv.org/abs/2305.16939