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 for which a mathematical solution is known, and add 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) can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as
asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one.