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arXiv:1409.0518 · Physica Scripta

PT-/non-PT-symmetric and non-Hermitian Hellmann potential: approximate bound and scattering states with anyℓ-values

Altuğ Arda, Ramazan Sever

Published Aug 28, 2014• 2 citations
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Abstract

We investigate the approximate bound state solutions of the Schrödinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained. Numerical values of energy eigenvalues for the bound states are compared with the ones obtained before. Scattering state solutions are also studied. Phase shifts of the potential are written in terms of the angular momentum quantum number $\ell$.

DOI
10.1088/0031-8949/89/10/105204

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PT-/NON-PT-SYMMETRIC AND NON-HERMITIAN HELLMANN POTENTIAL: APPROXIMATE BOUND AND SCATTERING STATES WITH ANY ℓ-VALUES

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We investigate the approximate bound state solutions of the Schr\"odinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained. Numerical values of energy eigenvalues for the bound states are compared with the ones obtained before. Scattering state solutions are also studied. Phase shifts of the potential are written in terms of the angular momentum quantum number $\ell$.

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Comment on: ‘PT-/non-PT-symmetric and non-Hermitian Hellmann potential: approximate bound and scattering states with anyℓ-values’

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We carry out an analysis of the paper published in Arda and Sever (2014 Phys. Scr. 89 105204 ) and reveal several unclear points. In the first place, the derivation of the main equations does not appear to be correct. In the second place, the expression for the energy does not appear to yield the results reported by the authors. In the third place, they failed to indicate the references reporting the eigenvalues chosen for comparison. In the fourth place the eigenvalues reported by the authors do not show the same order as those of the Hellmann potential thus leading to a different underlying physics. What is more: the spectrum of the modified model is qualitatively different from the one supported by the Hellmann potential.

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arXiv:quant-ph/0508009•Aug 1, 2005•6 citations
We investigate the approximate bound state solutions of the Schrödinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained. Numerical values of energy eigenvalues for the bound states are compared with the ones obtained before. Scattering state solutions are also studied. Phase shifts of the potential are written in terms of the angular momentum quantum number ℓ\ellℓ.
We investigate the approximate bound state solutions of the Schr\"odinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained. Numerical values of energy eigenvalues for the bound states are compared with the ones obtained before. Scattering state solutions are also studied. Phase shifts of the potential are written in terms of the angular momentum quantum number ℓ\ellℓ.
We carry out an analysis of the paper published in Arda and Sever (2014 Phys. Scr. 89 105204 ) and reveal several unclear points. In the first place, the derivation of the main equations does not appear to be correct. In the second place, the expression for the energy does not appear to yield the results reported by the authors. In the third place, they failed to indicate the references reporting the eigenvalues chosen for comparison. In the fourth place the eigenvalues reported by the authors do not show the same order as those of the Hellmann potential thus leading to a different underlying physics. What is more: the spectrum of the modified model is qualitatively different from the one supported by the Hellmann potential.