Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

American Journal of Physics

Introductory Quantum Mechanics with the Computer

John R. Merrill

Published Jan 1, 1972• 13 citations
Publisher

Abstract

This paper presents a way to use a computer in the teaching of introductory, stationary state, Schrödinger quantum mechanics. The method is based upon an easily explained computer method; a 20-line program in BASIC is presented to implement the strategy. Not only is this numerical technique completely general for all one-dimensional and all spherically symmetric, three-dimensional problems, but also it allows the student to be introduced to topics of interest such as asymptotic solutions. Several examples of the use of the computer technique are presented.

DOI
10.1119/1.1986460

Related papers

Computer Solutions to a Realistic “One-Dimensional” Schrödinger Equation

Jay Sharon Bolemon

An important technique for teaching introductory wave mechanics is provided by the numerical calculation of stationary state solutions of the Schrödinger equation. Realistic problems in wave mechanics that do not require sophisticated computer techniques are very valuable for the instruction of undergraduates. In the central-field model for atoms, the calculation of electron states reduces to the solution of a one-dimensional differential equation whose numerical solutions are no more difficult to obtain than those for a finite square well. A method used by our students is discussed in this paper for the calculation of the electron wavefunctions in a central-field potential. By working this problem, students obtain meaningful results that give them insight into the theory of atomic structure. Results of their experience are included, and possibilities of extending this example are discussed.

American Journal of Physics•Oct 1, 1972•13 citations

Introductory Quantum Mechanics Using Maple V

Yutaka Abe

This article discusses a set of Maple programs developed to reinforce understanding of basic concepts presented in an introductory quantum mechanics course. It was designed so that the solutions of the problems were analytically tractable as well as numerically obtainable. We note that there exist various approaches to a simple quantum mechanical problem. For example, for the problem of bound-states with a one-dimensional potential, the transfer matrix method, the Laplace transform method, and the Feynman path integral method can equally be applied. We believe that this type of program is extremely useful for igniting the student’s interest and widening his or her viewpoint. Several examples, such as the solution of various one-dimensional potential problems and the solution of the one-dimensional Schroedinger wave equation, are discussed in order to indicate how constructive reinforcement is established.

Birkhäuser Boston eBooks•Jan 1, 1993•1 citation

Playing with a Quantum Computer

Rainer Müller, Franziska Greinert

The high public attention given to quantum computing shows that it is perceived as an interesting topic. We want to utilize this motivating effect for the teaching and learning of quantum physics. Specifically, we want to take advantage of the access to real quantum computers, which various providers make available free of charge. We show a direct and straightforward way to use quantum computers in an introductory course on quantum physics. We use an algorithm that solves a simple and easily understandable problem while providing a quantum advantage. The algorithm we propose is a simple game in which the use of quantum physics offers a winning advantage. The game is called Quantum Penny Flip and was proposed by David A. Meyer back in 1999. It can be easily reformulated to be described by quantum gates. We can therefore use it to teach the programming of a quantum computer. We demonstrate its implementation in IBM's Quantum Composer.

arXiv:2108.06271•Aug 13, 2021•3 citations

The Schrödinger Equation

Sølve Selstø

This concise textbook introduces an innovative computational approach to quantum mechanics. Over the course of this engaging and informal book, students are encouraged to take an active role in learning key concepts by working through practical exercises. The book equips readers with some basic methodology and a toolbox of scientific computing methods, so they can use code to simulate and directly visualize how quantum particles behave. The important foundational elements of the wave function and the Schrödinger equation are first introduced, then the text gradually builds up to advanced topics including relativistic, open, and non-Hermitian quantum physics. This book assumes familiarity with basic mathematics and numerical methods, and can be used to support a two-semester advanced undergraduate course. Source code and solutions for every book exercise involving numerical implementation are provided in Python and MATLAB®, along with supplementary data. Additional problems are provided online for instructor use with locked solutions.

Cambridge University Press eBooks•Apr 24, 2024•0 citations

Computations in quantum mechanics made easy

H. J. Korsch, Kevin Rapedius

Abstract Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.

arXiv:1603.04167•European Journal of Physics•Aug 3, 2016•11 citations

Brief Introduction to Quantum Computing for Undergraduate Students: Lecture One

Li Chen

This article provides an introductory overview of quantum computing for college students through intuitive examples. We explore key concepts, starting with the basic principles of quantum mechanics. The discussion covers essential elements such as Qubits, superposition, entanglement, and introduces quantum gates. The article concludes by examining the first quantum algorithm: the solution to Deutsch's Problem.

ACM SIGACT News•Mar 26, 2024•3 citations
This paper presents a way to use a computer in the teaching of introductory, stationary state, Schrödinger quantum mechanics. The method is based upon an easily explained computer method; a 20-line program in BASIC is presented to implement the strategy. Not only is this numerical technique completely general for all one-dimensional and all spherically symmetric, three-dimensional problems, but also it allows the student to be introduced to topics of interest such as asymptotic solutions. Several examples of the use of the computer technique are presented.
An important technique for teaching introductory wave mechanics is provided by the numerical calculation of stationary state solutions of the Schrödinger equation. Realistic problems in wave mechanics that do not require sophisticated computer techniques are very valuable for the instruction of undergraduates. In the central-field model for atoms, the calculation of electron states reduces to the solution of a one-dimensional differential equation whose numerical solutions are no more difficult to obtain than those for a finite square well. A method used by our students is discussed in this paper for the calculation of the electron wavefunctions in a central-field potential. By working this problem, students obtain meaningful results that give them insight into the theory of atomic structure. Results of their experience are included, and possibilities of extending this example are discussed.
This article discusses a set of Maple programs developed to reinforce understanding of basic concepts presented in an introductory quantum mechanics course. It was designed so that the solutions of the problems were analytically tractable as well as numerically obtainable. We note that there exist various approaches to a simple quantum mechanical problem. For example, for the problem of bound-states with a one-dimensional potential, the transfer matrix method, the Laplace transform method, and the Feynman path integral method can equally be applied. We believe that this type of program is extremely useful for igniting the student’s interest and widening his or her viewpoint. Several examples, such as the solution of various one-dimensional potential problems and the solution of the one-dimensional Schroedinger wave equation, are discussed in order to indicate how constructive reinforcement is established.
The high public attention given to quantum computing shows that it is perceived as an interesting topic. We want to utilize this motivating effect for the teaching and learning of quantum physics. Specifically, we want to take advantage of the access to real quantum computers, which various providers make available free of charge. We show a direct and straightforward way to use quantum computers in an introductory course on quantum physics. We use an algorithm that solves a simple and easily understandable problem while providing a quantum advantage. The algorithm we propose is a simple game in which the use of quantum physics offers a winning advantage. The game is called Quantum Penny Flip and was proposed by David A. Meyer back in 1999. It can be easily reformulated to be described by quantum gates. We can therefore use it to teach the programming of a quantum computer. We demonstrate its implementation in IBM's Quantum Composer.
This concise textbook introduces an innovative computational approach to quantum mechanics. Over the course of this engaging and informal book, students are encouraged to take an active role in learning key concepts by working through practical exercises. The book equips readers with some basic methodology and a toolbox of scientific computing methods, so they can use code to simulate and directly visualize how quantum particles behave. The important foundational elements of the wave function and the Schrödinger equation are first introduced, then the text gradually builds up to advanced topics including relativistic, open, and non-Hermitian quantum physics. This book assumes familiarity with basic mathematics and numerical methods, and can be used to support a two-semester advanced undergraduate course. Source code and solutions for every book exercise involving numerical implementation are provided in Python and MATLAB®, along with supplementary data. Additional problems are provided online for instructor use with locked solutions.
Abstract Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of spectral and dynamical properties for one-dimensional and two-dimensional single-particle systems as well as bosonic many-particle and open quantum systems. Due to their technical simplicity these methods are well suited as a tool for teaching quantum mechanics to undergraduates and graduates. Explicit implementations of the presented numerical methods in Matlab are given.