Perturbation (Quantum dynamics)

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, known system. The idea is to start with a simple system for which a mathematical solution is known (e.g. the time-independent Schrödinger equation: H ^ | Ψ ⟩ = E | Ψ ⟩ {\displaystyle {\hat {H}}|\Psi \rangle =E|\Psi \rangle } ) and add an additional "perturbing" Hamiltonian ( H ′ {\displaystyle H'} ) representing a weak disturbance to the known system to the original Hamiltonian ( H 0 {\displaystyle H_{0}} ) of the known system (i.e. H ^ = H 0 + H ′ {\displaystyle {\hat {H}}=H_{0}+H'} ). If the disturbance is small, the new energy levels and eigenstates of the perturbed system can be expressed as "corrections" to the known energy levels and eigenstates of the simpler system. These corrections can be made at progressively smaller orders of magnitude until an n-th order that is so small a correction that it is negligible to the accuracy of the approximation.