Perturbation theory expands a quantum problem around a solvable Hamiltonian. Time-independent perturbation theory expands stationary energies and eigenstates; time-dependent perturbation theory expands dynamical amplitudes and transitions.
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Perturbation theory in quantum mechanics is a mathematical method used to find an approximate solution to a problem that cannot be solved exactly. It is particularly useful when the Hamiltonian (the total energy operator) of a quantum system can be expressed as the sum of a solvable part and a "perturbing" part that represents a small deviation from that solvable system. ### Key Concepts 1.