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Quantum Simulation Open Quantum Systems Decoherence

Exact normalized eigenfunctions for general deformed Hulthén potentials

arXiv

Authors: Richard L. Hall, Nasser Saad, K. D. Sen

Year

2018

Paper ID

22677

Status

Preprint

Abstract Read

~2 min

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Abstract

The exact solutions of Schrödinger's equation with the deformed Hulthén potential V_q(x)=-{μ e^{-δ x}}/\({1-q e^{-δ x}}\), δ,μ, q>0 are given, along with a closed--form formula for the normalization constants of the eigenfunctions for arbitrary q>0. The Crum-Darboux transformation is then used to derive the corresponding exact solutions for the extended Hulthén potentials V(x)= -{μ e^{-δ x}}/\({1-q e^{-δ x}}\)+ {q j(j+1) e^{-δ x}}/\({1-q e^{-δ x}}\)², j=0,1,2,dots. A general formula for the new normalization condition is also provided.

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The exact solutions of Schrödinger's equation with the deformed Hulthén potential Vq(x)=-μ e^-δ x /(1-q e^-δ x), δ,μ, q>0 are given, along with a closed--form formula for the...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1812.06383 [2] arXiv https://arxiv.org/abs/1812.06383 [3] Publisher https://arxiv.org/abs/1812.06383

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