Stationary State Perturbation Theory

Rayleigh-Schrödinger perturbation theory, where Hamiltonian can be split in a large, exactly solvable and a small part, is discussed in this chapter. First, theory is developed when unperturbed state is non-degenerate. Shifts in energy and wave function up to second order in perturbation strength have been calculated. This is applied to a perturbed harmonic oscillator and ground state of He-like atoms. Next theory is modified when unperturbed state is two fold degenerate, also up to second order. This is applied to Stark effect for first excited states of H-atom and also to the first excited state of He atom. Finally, the case when unperturbed state is N-fold degenerate has been treated.