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November 2019 Issue,

Volume 87, No. 11

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We show how to visualize the process of diagonalizing the Hamiltonian matrix to find the energy eigenvalues and eigenvectors of a generic one-dimensional quantum system. Starting in the familiar sine-wave basis of an embedding infinite square well, we display the Hamiltonian matrix graphically with the basis functions alongside. Each step in the diagonalization process consists of selecting a nonzero off-diagonal matrix element and then rotating the two corresponding basis vectors in their own subspace until this element is zero. We provide mathematica code to display the effects of these rotations on both the matrix and the basis functions. As an electronic supplement, we also provide a javascript web app to interactively carry out this process.

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NOTES AND DISCUSSIONS

Alexey V. Borisov, Alexander A. Kilin and Ivan S. Mamaev. DOI: 10.1119/10.0000006

PAPERS

by Kevin Randles, Daniel V. Schroeder and Bruce R. Thomas. DOI: 10.1119/10.0000014

by J. Franklin and Gopal Goel. DOI: 10.1119/1.5124814

by Jonathan Bougie and Asim Gangopadhyaya. DOI: 10.1119/1.5125213

by Deepa N. Chari, Hai D. Nguyen, Dean A. Zollman and Eleanor C. Sayre. DOI: 10.1119/1.5120392

by Kevin Krisciunas. DOI: 10.1119/1.5120020

by Joshua Zhou and Takyiu Liu. DOI: /10.1119/1.5124975

by Loris Ferrari. DOI: 10.1119/1.5124976

by R. Hauko and R. Repnik. DOI: 10.1119/1.5124978

by Timothy H. Boyer. DOI: 10.1119/1.5123158

by Sálvio Jacob Bereta, Lucas Madeira, Vanderlei S. Bagnato and Mônica A. Caracanhas. DOI: 10.1119/1.5125092

BOOK REVIEWS

by Allan Walstad. DOI: 10.1119/1.5121386

BOOKS RECEIVED

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