UBC Theses and Dissertations

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UBC Theses and Dissertations

Calculation of matrix elements for diatomic molecules Buckmaster, Harvey Allen


A number of potentials have been suggested as approximations to the 'true' potential function for the nuclei of a diatomic molecule. The relative merits of these potentials are discussed. Whenever possible the eigenfunctions and eigenvalues corresponding to these potentials are given. For the Morse potential the calculations of the eigenfunctions and eigenvalues are reproduced in detail. These eigenfunctions are used to derive general formulae for the radial parts of the dipole and quadrupole matrix elements. The expression for the dipole matrix element is [formula omitted] and for the quadrupole matrix element [formula omitted] The symbols are defined in sections 20, 21, and 22, The expression for M[subscript D] is in agreement with the one derived by Infeld and Hull while the expression for M[subscript Q] is a result which, so far as the author is aware, has not been published in the literature.

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