A Python Program for Solving Schro¨dinger's Equation in Undergraduate Physical Chemistry

Autor/inn/en	Srnec, Matthew N.; Upadhyay, Shiv; Madura, Jeffry D.
Titel	A Python Program for Solving Schro¨dinger's Equation in Undergraduate Physical Chemistry
Quelle	In: Journal of Chemical Education, 94 (2017) 6, S.813-815 (3 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Srnec, Matthew N.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0021-9584
DOI	10.1021/acs.jchemed.7b00003
Schlagwörter	Undergraduate Study; College Science; Chemistry; Science Instruction; Undergraduate Students; Quantum Mechanics; Equations (Mathematics); Programming Languages; Physics; Scientific Concepts; Energy; Mathematical Models + Suchen Sie Ihr Suchwort? Grundstudium; Chemie; Teaching of science; Science education; Natural sciences Lessons; Naturwissenschaftlicher Unterricht; Quantenmechanik; Equations; Mathematics; Gleichungslehre; Physik; Energie; Mathematical model; Mathematisches Modell
Abstract	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. (As Provided).
Anmerkungen	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: eic@jce.acs.org; Web site: http://pubs.acs.org/jchemeduc
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01