Perturbation theory in quantum mechanics

Summary

Perturbation theory in quantum mechanics computes the eigenvalues and eigenvectors of a Hamiltonian $H_0 + \lambda V$ as power series in a small parameter $\lambda$. It starts from the known solution for $H_0$. The time-independent version, the Rayleigh–Schrödinger series, gives energy shifts; the time-dependent version, the Dyson series, gives transition amplitudes. It is the main tool for systems that are close to an exactly solvable one. Its mathematical side is the perturbation theory of linear operators, which says when the series converge.