The use of Laplace transform in the inverse problem from bound states

IF 2.1 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Romanian Reports in Physics Pub Date : 2023-09-15 DOI:10.59277/romrepphys.2023.75.114
R. MEZHOUD, I. AMI, R. J. LOMBARD
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Abstract

"In a previous work dedicated to non-relativistic quantum mechanics in the three-dimensional space with spherical symmetry, we have shown the possibility of reconstructing the ground state density from its moments in the case of bound states. The method is based on relationships connecting these moments to the lower energy of each state of angular momentum `. The ground state density yields the ground state wave function, which allows us to calculate the equivalent local potential by inverting the Schrodinger equation. This calculus uses the Fourier transform of the ground state density ρ(r). The aim of this work is to check how to improve the results by replacing the Fourier transform by the Laplace transform of the quantity r2 ρ(r). The method is first presented. Then examples and results are compared to those obtained previously. "
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拉普拉斯变换在束缚态反问题中的应用
“在之前的一项研究球面对称三维空间中的非相对论量子力学的工作中,我们已经展示了从束缚态的矩重建基态密度的可能性。该方法基于将这些力矩与角动量的每个状态的较低能量联系起来的关系。基态密度产生基态波函数,它允许我们通过反演薛定谔方程来计算等效的局域势。这个微积分使用了基态密度ρ(r)的傅里叶变换。这项工作的目的是检查如何通过用r2 ρ(r)的拉普拉斯变换代替傅里叶变换来改进结果。本文首次提出了该方法。然后将实例和结果与之前的结果进行了比较。
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来源期刊
Romanian Reports in Physics
Romanian Reports in Physics 物理-物理:综合
CiteScore
4.20
自引率
29.60%
发文量
0
审稿时长
4-8 weeks
期刊介绍: Romanian Reports in Physics is a journal publishing physics contributions in the fields of: 1. Mathematical and General Physics 2. Nuclear Physics. Particle Physics. Astroparticle Physics 3. Atomic and Molecular Physics 4. Plasma Physics 5. Condensed Matter 6. Optics & Quantum Electronics 7. Biophysics & Medical Physics. Environmental Physics 8. Physical Methods and Instrumentation 9. Earth Physics
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