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 Simon Fraser University, Canada monagan@cecm.sfu.ca |
John F. Ogilvie Simon Fraser University, Canada ogilvie@cecm.sfu.ca |