Algorithm of Rayleigh–Schrödinger perturbation theory for hermitian operators

A simple algorithm of perturbation theory is obtained for an Hermitian operator $H=H^0+V$, where $V=A_1+A_2+\dots+A_n+\cdots$ and $A_n$ is an operator of $n$-th order with respect to a set of small parameters. The multiplicity of degeneracy of the unperturbed level is arbitrary. The scheme can be used, for example, in the problem of vibrational-rotational coupling in molecules. This is illustrated for the example of a triatomic linear symmetric molecule.