The diatomic anharmonic oscillator according to matrix mechanics1Expanded version of a talk presented at the Applied Computer Algebra meeting in Maui, August 1997. This work was supported by NSERC of Canada.1

We determine the energies of states of the diatomic anharmonic oscillator by matrix mechanics in its original form as developed by Heisenberg, Born and Jordan using perturbation theory in successive orders. We present exact formulae for the second-, fourth-, and sixth-order contributions to the energy that were computed with Maple. The calculations involve matrices of finite rank with symbolic entries. We include the Maple programs.