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ERIC Number: EJ1442278
Record Type: Journal
Publication Date: 2022-Aug
Pages: 8
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0021-9584
EISSN: EISSN-1938-1328
Available Date: N/A
Visualizing Solutions of the One-Dimensional Schrödinger Equation Using a Finite Difference Method
Arthur M. Halpern; Yingbin Ge; Eric D. Glendening
Journal of Chemical Education, v99 n8 p3053-3060 2022
FINDIF is a Windows application that numerically solves the one-dimensional (1D) Schrödinger equation and displays the eigenstates, eigenvalues, and probability density of the system. FINDIF accepts both nonperiodic and periodic 1D potential energy functions as input and uses the finite difference method to evaluate the energy of the quantum system. This Technology Report illustrates the use of FINDIF with applications, such as the classic 1D particle-in-a-box, the particle-in-a-box with internal barrier, the modified Kronig-Penney model of a linear array of rectangular wells, the harmonic oscillator with visualization of the eigenstates and tunneling effect, the anharmonic Morse potential of the Ar dimer, and the periodic torsional potential for internal rotation of ethane. Students can explore other quantum chemical examples by considering both realistic and fictitious model potential energy functions, making outcome predictions before running FINDIF calculations, visualizing the results afterward, and then comparing their predictions with the results they observe. Such exercises assist students as they develop insights into the behavior and properties of quantum mechanical systems.
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
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Author Affiliations: N/A