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2000
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Research: Science and Education
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Advanced Chemistry Classroom and Laboratory
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Variational Principle for a Particle in a Box
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Juan I. Casaubon
Facultad de Ciencias Exactas y Naturales, Universidad de Belgrano y CONICET, Villanueva 1324, 1426 Buenos Aires, Argentina
Graham Doggett
Chemistry Department, University of York, Heslington, York YO10 5DD, UK
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September 2000
Vol. 77 No. 9
p. 1221
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| Abstract |
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The particle-in-a-box problem is reexamined, using different model wave functions, to illustrate the use of the variational principle applied to the simplest solvable quantum mechanical problem. The scheme presented here provides a useful paradigm for the LCAO approach used in atomic and molecular calculations. Suitable polynomial basis functions are introduced that provide a way for controlling both the accuracy and the number of independent variational parameters used in the energy calculations, when the coordinate origin is taken either at the left-hand edge or the center of the box. Links with the Bransden and Joachain calculations on the first two even parity states are made. The approximate ground state wave function, x(x - L), is also redefined by introducing a variation parameter in the form of a prescription based on the value of the position coordinate. Finally, a straightforward method is presented for determining an approximate energy for an arbitrary excited state, based on the use of any approximate ground state wave function.
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| More Information |
 Citation |
Casaubon, Juan I.; Doggett, Graham. J. Chem. Educ. 2000 77 1221.
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Keywords |
Teaching/Learning Theory/Practice; Quantum Chemistry; Teaching / Learning Aids
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History |
Created:
Last Updated: |
August 29, 2000
June 22, 2005
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| Home > JCE Print > Journal of Chemical Education > Issues >
2000
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September
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1221
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