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                    Grand Challenges in Computer Algebra
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      The Diatomic Anharmonic Oscillator According to Matrix Mechanics

     The model of a vibrating diatomic molecule as an anharmonic oscillator
     is investigated with matrix mechanics and perturbation theory of high
     orders. Using the commutation properties of matrices that represent
     coordinate and momentum, with the commutation law applied explicitly
     for the harmonic oscillator, we solve the eigenvalue problem taking
     successive anharmonic terms in the function for potential energy in
     successive orders of perturbation theory. We use Maple to solve the
     sets of linear equations and to seek general relations for the matrix
     elements of the hamiltonian and unitary matrices to diagonalise the
     hamiltonian.

     Michael B. Monagan                         John F. Ogilvie
     Simon Fraser University,                   Simon Fraser University,
     Canada                                     Canada
     monagan@cecm.sfu.ca                        ogilvie@cecm.sfu.ca

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Last update: May 29, 1997
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