New Wine in Old Bottle: An Improved Perspective on the Greene-Aldrich Approximation for the Generalized Pöschl-Teller Potential

IF 0.4 4区 物理与天体物理 Q4 PHYSICS, MULTIDISCIPLINARY Russian Physics Journal Pub Date : 2024-08-27 DOI:10.1007/s11182-024-03234-w
P. Rajesh Kumar
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Abstract

The generalized Pöschl–Teller potential is well-known and is widely applied in molecular physics, chemistry, and nonlinear physics. In the past, when the vintage Greene–Aldrich approximation scheme for the centrifugal potential of the generalized Pöschl–Teller potential was examined, the consensus was that it would break down or become unreliable for large values of the potential parameter α. However, this study challenges that perspective by reviewing the problem in a new light and proposing a new and improved Greene–Aldrich approximation that mitigates the breakdown effect. Additionally, it is demonstrated that the energy eigenvalues produced for short and long-range potentials are in considerably closer agreement with those obtained using the numerical integration method than with the results of earlier research.

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旧瓶装新酒:广义波氏势的格林-阿尔德里希近似法的改进视角
广义波氏-泰勒势是众所周知的,并广泛应用于分子物理学、化学和非线性物理学。过去,在研究广义波氏势的离心势的古老格林-奥尔德里奇近似方案时,人们一致认为当势参数 α 的值很大时,该方案就会崩溃或变得不可靠。然而,本研究挑战了这一观点,从新的角度审视了这一问题,并提出了一种新的改进型格林-奥尔德里奇近似方案,以减轻崩溃效应。此外,本研究还证明了短程和长程电势的能量特征值与使用数值积分方法得到的能量特征值的一致性比早期研究的结果要好得多。
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来源期刊
Russian Physics Journal
Russian Physics Journal PHYSICS, MULTIDISCIPLINARY-
CiteScore
1.00
自引率
50.00%
发文量
208
审稿时长
3-6 weeks
期刊介绍: Russian Physics Journal covers the broad spectrum of specialized research in applied physics, with emphasis on work with practical applications in solid-state physics, optics, and magnetism. Particularly interesting results are reported in connection with: electroluminescence and crystal phospors; semiconductors; phase transformations in solids; superconductivity; properties of thin films; and magnetomechanical phenomena.
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