Numerical approach to the Schroumldinger equation in momentum space

被引：6
作者：
Karr, William A. [1 ]
Jamell, Christopher R. [1 ]
Joglekar, Yogesh N. [1 ]
机构：
[1] Indiana Univ Purdue Univ, Dept Phys, Indianapolis, IN 46202 USA
来源：
AMERICAN JOURNAL OF PHYSICS | 2010年 / 78卷 / 04期
基金：
美国国家科学基金会;
关键词：
integral equations; matrix algebra; physics education; quantum theory; Schrodinger equation; teaching; 2; DIMENSIONS; SCHRODINGER-EQUATION; QUANTUM-MECHANICS; HYDROGEN-ATOM; SCATTERING; MODEL;
D O I：
10.1119/1.3272021
中图分类号：
G40 [教育学];
学科分类号：
040101 ; 120403 ;
摘要：
The treatment of the time-independent Schroumldinger equation in real space is an indispensable part of introductory quantum mechanics. In contrast, the Schroumldinger equation in momentum space is an integral equation that is not readily amenable to an analytical solution and is rarely taught. We present a numerical approach to the Schroumldinger equation in momentum space. After a suitable discretization process, we obtain the Hamiltonian matrix and diagonalize it numerically. By considering a few examples, we show that this approach is ideal for exploring bound states in a localized potential and complements the traditional (analytical or numerical) treatment of the Schroumldinger equation in real space.
引用
收藏
页码：407 / 411
页数：5
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