framework for simplifying a difficult problem by finding an approximate solution that is subsequently refined as more details, initially ignored, are systematically included.
A physical theory which applies to nature is necessarily a rather complicated object, even if the underlying principle behind it is simple and beautiful. Therefore to examine the detailed physics which the theory predicts requires some kind of approximation. Perturbation theory is a type of approximation whereby one expands the equations in powers of some small parameter, much like a decimal expansion is an expansion in powers of 1/10th. If there is a suitable small parameter in the theory then perturbation techniques can be very successful. However, if there is no such parameter then perturbation theory will fail and in general there is no known alternative. Even if a perturbative parameter is available it is inevitable that some physics will be obscured by the perturbative expansion. The confinement of quarks into protons and neutrons and high temperature super-conductivity are examples of phenomena for which perturbative techniques have failed. Thus the understanding of non-perturbative effects is an important if not crucial goal for physics.
approximation to include electron correlation, based on Taylor Series expansion of the Hartree-Fock wavefunction (1 e- Hamiltonian) as the 0th order wavefunction, for E in Schrödinger equation, truncated after n terms.
The systematic derivation of linearized equations of systems by the method of small perturbations, exhibiting the assumptions involved; or any model derived by use of this method.
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system and gradually turn on an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) will be continuously generated from those of the simple system.