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arXiv · 1901.01702

Convergent perturbation expansion of energy eigenfunctions on unperturbed basis states in classically-forbidden regions

Jiaozi Wang·Wen-ge Wang
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Abstract

We study properties of eigenfunctions of perturbed systems, given on the eigenbases of unperturbed, integrable systems. For a given pair of perturbed and unperturbed systems, with respect to the energy of each perturbed state, the unperturbed basis states can be divided into two groups: one in the classically-allowed region and the other in the classically-forbidden region; correspondingly, the eigenfunction of the perturbed state is also divided into two parts. In the semiclassical limit, it is shown that, making use of components of the eigenfunction in its classically-allowed region, its components in the classically-forbidden region can be written in the form of a convergent perturbation expansion, which is valid for all perturbation strengths.

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Jiaozi Wang, Wen-ge Wang. 2019-01-07. Convergent perturbation expansion of energy eigenfunctions on unperturbed basis states in classically-forbidden regions. https://doi.org/10.1088/1751-8121/ab1c07

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