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
相关论文
共 50 条
  • [41] The Klein-Gordon equation with the Kratzer potential in the noncommutative space
    Darroodi, M.
    Mehraban, H.
    Hassanabadi, S.
    MODERN PHYSICS LETTERS A, 2018, 33 (35)
  • [42] A fast method for solving both the time-dependent Schroumldinger equation in angular coordinates and its associated "m-mixing" problem
    Reuter, Matthew G.
    Ratner, Mark A.
    Seideman, Tamar
    JOURNAL OF CHEMICAL PHYSICS, 2009, 131 (09)
  • [43] Numerical solution for space and time fractional order Burger type equation
    Yokus, Asif
    ALEXANDRIA ENGINEERING JOURNAL, 2018, 57 (03) : 2085 - 2091
  • [44] A New Feature of the Screened Coulomb Potential in Momentum Space
    Watanabe, Takashi
    Hiratsuka, Yasuhisa
    Oryu, Shinsho
    Togawa, Yoshio
    FEW-BODY SYSTEMS, 2017, 58 (02)
  • [45] Laguerre Wavelet Approach for a Two-Dimensional Time-Space Fractional Schrodinger Equation
    Bekiros, Stelios
    Soradi-Zeid, Samaneh
    Mou, Jun
    Yousefpour, Amin
    Zambrano-Serrano, Ernesto
    Jahanshahi, Hadi
    ENTROPY, 2022, 24 (08)
  • [46] Generalized space and linear momentum operators in quantum mechanics
    da Costa, Bruno G.
    Borges, Ernesto P.
    JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (06)
  • [47] Efficient numerical approach for solving the diffusion equation with variable coefficients
    Liemert, Andre
    Reitzle, Dominik
    Kienle, Alwin
    OPTICAL ENGINEERING, 2022, 61 (02)
  • [48] An Analytical and Numerical Approach to Solve the Tsunami Wave Propagation Equation
    Kesarwani, Juhi
    Majumder, Abhijit
    Sharma, Ishita
    Kesarwany, Ashish Kumar
    CONTEMPORARY MATHEMATICS, 2025, 6 (01): : 412 - 424
  • [49] Analytical and numerical aspects of the linear and non-linear Schrodinger equation
    Negulescu, Claudia
    RIVISTA DI MATEMATICA DELLA UNIVERSITA DI PARMA, 2019, 10 (02): : 351 - 446
  • [50] A unified momentum equation approach for computing thermal residual stresses during melting and solidification
    Yeo, Haram
    Ki, Hyungson
    COMPUTER PHYSICS COMMUNICATIONS, 2018, 224 : 230 - 244
12345