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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
Abstract Words
93
Citations
N/A
Abstract
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 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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