Perturbation Theory Derivations
Perturbation derivations are assumption-sensitive. Always check the small parameter, spectral gap, degeneracy structure, time scale, and error estimate before importing a formula.
Time-Independent Perturbation Theory
Section titled “Time-Independent Perturbation Theory”- Nondegenerate Perturbation Theory
- Degenerate Perturbation Theory
- Brillouin-Wigner Perturbation Theory
- Anharmonic Oscillator
Time-Dependent Perturbations
Section titled “Time-Dependent Perturbations”- First-Order Transition Probability
- Harmonic Perturbations
- Fermi’s Golden Rule
- Landau-Zener Transition
Variational and Semiclassical Methods
Section titled “Variational and Semiclassical Methods”Effective Hamiltonians and Scale Separation
Section titled “Effective Hamiltonians and Scale Separation”- Magnus Expansion
- Floquet-Magnus Expansion
- Rotating-Wave Approximation
- Schrieffer-Wolff Transformation
- Feshbach Projection Formalism
References
Section titled “References”- A. Messiah, Quantum Mechanics, Dover, 1999.
- C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics, Wiley, 1977.
- C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, Springer, 1999.