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Accuracy and efficiency of a phase function method solving the first-order nonlinear one-dimensional radial Schrodinger equation.

机译：求解一阶非线性一维径向薛定inger方程的相位函数方法的精度和效率。

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Phase shifts are used to calculate the quantum mechanical scattering cross section of a particle by a spherically symmetrical potential. Accurate phase shifts for elastic scattering from a central potential can be calculated via a phase function. Results using this approach are more accurate than methods based on classical "mechanics".;The problem of finding numerical solutions of the radial Schrodinger equation with a positive energy is a subject of great interest. A phase function method created to find solutions in the asymptotic region where the potential is negligible is studied.;The purpose of this dissertation is to evaluate a variable phase method for obtaining phase shifts. MATHEMATICA 4.1., a high-level programming language is used to construct programs to compare the efficiency and accuracy of the variable phase function method with that of the wave function method. These programs are designed for ease of use for choices of the input parameters and the potential function. Numerical results are based on scattering from the Lennard -Jones (12, 6) potential.

机译：相移用于通过球对称电势来计算粒子的量子机械散射截面。可以通过相位函数计算出从中心电位进行弹性散射的准确相移。使用这种方法的结果比基于经典“力学”的方法更准确。找到具有正能量的径向Schrodinger方程的数值解的问题是一个非常令人感兴趣的问题。研究了一种在电位可忽略的渐近区域中寻找解的相函数方法。本文的目的是评估一种可变相方法以获得相移。 MATHEMATICA 4.1。是一种高级编程语言，用于构建程序，以比较可变相位函数方法和波动函数方法的效率和精度。这些程序的设计易于使用，可以选择输入参数和潜在功能。数值结果基于Lennard -Jones（12，6）势的散射。

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作者
Smith, Karl Nicholas.;
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作者单位

Polytechnic Institute of New York University.;

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授予单位 Polytechnic Institute of New York University.;
学科 Physics Astrophysics.;Physics Atomic.;Physics Quantum.
学位 Ph.D.
年度 2010
页码 249 p.
总页数 249
原文格式 PDF
正文语种 eng
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1. Stationary solutions of the one-dimensional nonlinear Schrodinger equation. I. Case of repulsive nonlinearity - art. no. 063610 [J] . Carr LD., Reinhardt WP., Clark CW. Physical Review, A. Atomic, molecular, and optical physics . 2000,第6期

机译：一维非线性薛定inger方程的平稳解。 I.排斥非线性的情况-艺术。没有。 063610
2. Stationary solutions of the one-dimensional nonlinear Schrodinger equation. II. Case of attractive nonlinearity - art. no. 063611 [J] . Carr LD., Reinhardt WP., Clark CW. Physical Review, A. Atomic, molecular, and optical physics . 2000,第6期

机译：一维非线性薛定inger方程的平稳解。二。有吸引力的非线性情况-艺术。没有。 063611
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5. Improving the accuracy of the Generalized FDTD-Q scheme for solving the linear time-dependent Schrodinger equation. [D] . Elliott, James John, III. 2011

机译：提高广义FDTD-Q格式求解线性时变薛定inger方程的准确性。
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Accuracy and efficiency of a phase function method solving the first-order nonlinear one-dimensional radial Schrodinger equation.

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