Wronskian representation of second-order Darboux transformations for Schrdinger equations with quadratically energy-dependent potentials

Schulze-Halberg Axel; Paskash Matthew

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Wronskian representation of second-order Darboux transformations for Schrdinger equations with quadratically energy-dependent potentials

机译：具有二次能量依赖潜力的施拉网方程的二阶DARBOUX转换的WRONSKIAN表示

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摘要

We construct a Wronskian representation of second-order Darboux transformations for Schrdinger-type equations that feature quadratically energy-dependent potentials. Besides generalizing the conventional Darboux transformation of second order, our results can be adapted to generate zero-energy solutions to the massless Dirac equation in two dimensions.

机译：我们构建了用于施拉特型方程的二阶DARBOUX转换的WRONSKIAN表示，该方程具有二次电能相关的电位。除了推广常规DARBOUX转换的二阶的转换外，我们的结果可以适于为两个维度的无抽质DIDAC方程产生零能量解。

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来源
《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2020年第1期|共11页
作者
Schulze-Halberg Axel; Paskash Matthew;
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作者单位

Indiana Univ Northwest Dept Math &

Actuarial Sci 3400 Broadway Gary IN 46408 USA;

Univ Illinois Dept Econ 1407 West Gregory Dr Urbana IL 61801 USA;

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原文格式 PDF
正文语种 eng
中图分类物理学;
关键词
second-order Darboux transformation; Wronskian representation; massless Dirac equation; zero-energy solution;

机译：二阶DARBOUX转型;WRONSKIAN代表;无麻狄拉德方程;零能量解决方案;

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专利

1. Wronskian representation of second-order Darboux transformations for Schrdinger equations with quadratically energy-dependent potentials [J] . Schulze-Halberg Axel, Paskash Matthew Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2020,第1期

机译：具有二次能量依赖潜力的施拉网方程的二阶DARBOUX转换的WRONSKIAN表示
2. Darboux Transformations for Energy-Dependent Potentials and the Klein–Gordon Equation [J] . Axel Schulze-Halberg Mathematical Physics, Analysis and Geometry . 2013,第2期

机译：与能量有关的势能的Darboux变换和Klein-Gordon方程
3. Generalized Schrodinger equations with quadratical energy-dependence in the potential: Darboux transformations and application to the Heun class [J] . Schulze-Halberg Axel Journal of Mathematical Physics . 2020,第8期

机译：广义Schrodinger方程具有四重能量依赖性的潜力：Darboux转换和应用于Heun类
4. Darboux transformations and linear parabolic partial differential equations [C] . Arrigo, D.J., Hickling, . 2004

机译：Darboux变换和线性抛物型偏微分方程
5. A generalized approach to Darboux transformations for differential equations. [D] . Unlu, Mehmet. 2014

机译：微分方程Darboux变换的一种通用方法。
6. Principal Quadratic Functionals and Self-Adjoint Second-Order Differential Equations [O] . Walter Leighton 1949

机译：主二次函数和自伴二阶微分方程
7. A class of deformations of the Schrdinger representation of the Heisenberg commutation relation and exact solution to a Heisenberg equation and a Schrdinger equation [O] . Arai A, Kawano H 2000

机译：Heisenberg换向关系的Schrdinger表示的一类变形以及Heisenberg方程和Schrdinger方程的精确解

Wronskian representation of second-order Darboux transformations for Schrdinger equations with quadratically energy-dependent potentials

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