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ERIC Number: EJ1159642
Record Type: Journal
Publication Date: 2017-Jun
Pages: 3
Abstractor: As Provided
ISSN: ISSN-0021-9584
A Python Program for Solving Schro¨dinger's Equation in Undergraduate Physical Chemistry
Srnec, Matthew N.; Upadhyay, Shiv; Madura, Jeffry D.
Journal of Chemical Education, v94 n6 p813-815 Jun 2017
In undergraduate physical chemistry, Schrödinger's equation is solved for a variety of cases. In doing so, the energies and wave functions of the system can be interpreted to provide connections with the physical system being studied. Solving this equation by hand for a one-dimensional system is a manageable task, but it becomes time-consuming once students aim to make various changes and investigate the impact of those changes on the results. To address this challenge, numerical methods, such as the shooting and linear finite-difference methods, have been utilized to quickly solve Schrödinger's equation. In this technology report, we use the Python programming environment and the three-point finite-difference numerical method to find the solutions and plot the results (wave functions or probability densities) for a particle in an infinite, finite, double finite, harmonic, Morse, or Kronig-Penney finite potential energy well. We believe that this technology report will educate undergraduates on the basic tools of computer programming, data analysis, and making connections between mathematical models and the physical systems with which they are associated.
Division of Chemical Education, Inc and ACS Publications Division of the American Chemical Society. 1155 Sixteenth Street NW, Washington, DC 20036. Tel: 800-227-5558; Tel: 202-872-4600; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Grant or Contract Numbers: 1259941