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  Home > JCE Print > Journal of Chemical Education > Issues > 1998  > March  >
Research: Science and Education
Three-Dimensional Representation of Surface Spherical Harmonics and Their Squares Using Normal Projections: Some Comments on the Functions - Preparing for an Undergraduate Exercise
Rudolf Kiralj
Rudjer Boskovic Institute, P.O.B. 1016, Zagreb, Bijenicka 54 HR-10 001, CROATIA
Cover
March 1998
Vol. 75 No. 3
p. 332
Abstract
Surface spherical harmonics and their squares occur in quantum chemistry as angular wavefunctions and angular probability densities, respectively. These functions can be found in a large variety of physico-chemical problems dealing with spherical symmetry or spherical surfaces. Thus there is a great need for exact graphical representation of the harmonics. At the undergraduate level, the definition, interpretation or graphical representation of the harmonics found in various literature can be inaccurate or source of confusion. This article focus on some important concepts as the result of a literature survey regarding the definition of surface spherical harmonics and spherical coordinates, the classification of spherical harmonics, and the occurence of the surface spherical harmonics and their squares in various fields. Knowing these concepts, undergraduates are prepared to make their own exercises - three-dimensional drawings of surface spherical harmonics and their squares based on normal projections and mechanical hand-drawing. By this, students can overcome their visualization difficulties about the functions, learn more about their nature as well as the principles of graphical representation.
Supplement
Correction to Manuscript Cited in J. Chem. Educ. 1998, 75, 1387.
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*  Citation
 Kiralj, Rudolf. J. Chem. Educ. 1998 75 332.
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*  History
 Created:
Last Updated:		 June 28, 1999
November 22, 2005
Full Text PDF corrected (November 1998).
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