A Practical Method for the Solution of Certain Problems in Quantum Mechanics by Successive Removal of Terms from the Hamiltonian by Contact Transformations of the Dynamical Variables Part II. Power Series in a Coordinate and Its Conjugate Momentum. The Anharmonic Oscillator by Perturbation Theory

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Abstract
The non‐commutative algebra of polynomials in a coordinate and its conjugate momentum is reduced to common algebra by Weyl's method, and tables are given for facilitating its use. It is shown how the problem of the anharmonic oscillator can be solved by contact transformations, and tables are given for removing terms up to the third degree in its coordinate and momentum and for finding the modified Hamiltonian up to the fourth degree, which is as far as is ordinarily required in molecular theory. To illustrate the power of the method, the energy is computed up to terms of the eighth degree for energy containing terms to that degree (in the coordinate only), obtaining Dunham's result together with the constant terms of that order not given by him.

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