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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
Perturbation theory is an extremely important tool for describing real quantum systems, as it turns out to be very difficult to find exact solutions to the Schrödinger equation for Hamiltonians of even moderate complexity
perturbation is important to realize controlling of a circuit. it is important while doing fourier analysis... in example, we rectify an ac voltage, the output is composed of two components.first is dc component.other one is the ripple.we can call that ripple as perturbation.
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