在一般径向网格上的Schrödinger方程

IF 1.6 3区物理与天体物理 Q3 PHYSICS, FLUIDS & PLASMAS

High Energy Density Physics Pub Date : 2023-06-01 DOI:10.1016/j.hedp.2023.101042

Christopher Bowen , Jean-Christophe Pain

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引用次数: 0

摘要

在这篇笔记中，我们讨论了径向网格在Schrödinger方程数值解析中的选择。我们使用描述变量变化关系的显式或隐式形式，详细描述了一般径向网格的变量和函数变化引起的方程的变换，并将其应用于ar+bln(r)对数线性网格。结果表明，在前一种情况下，兰伯特W函数的前三个导数是必需的。如果我们采用隐式关系，就不需要这种复杂性了。

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Schrödinger equation on a generic radial grid

In this note, we discuss the choice of radial grid in the numerical resolution of the Schrödinger equation. We detail the transformation of the equation resulting from a change of variable and function for a generic radial grid, using either the explicit or implicit form of the relation describing the change of variable, and apply it to the $a r + b ln (r)$ log-linear mesh. It is shown that, in the former case, the first three derivatives of the Lambert $W$ function are required. This complication becomes unnecessary if we adopt the implicit relation instead.

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来源期刊

High Energy Density Physics PHYSICS, FLUIDS & PLASMAS-

CiteScore

4.20

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： High Energy Density Physics is an international journal covering original experimental and related theoretical work studying the physics of matter and radiation under extreme conditions. ''High energy density'' is understood to be an energy density exceeding about 1011 J/m3. The editors and the publisher are committed to provide this fast-growing community with a dedicated high quality channel to distribute their original findings. Papers suitable for publication in this journal cover topics in both the warm and hot dense matter regimes, such as laboratory studies relevant to non-LTE kinetics at extreme conditions, planetary interiors, astrophysical phenomena, inertial fusion and includes studies of, for example, material properties and both stable and unstable hydrodynamics. Developments in associated theoretical areas, for example the modelling of strongly coupled, partially degenerate and relativistic plasmas, are also covered.