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Perturbation theory refers to methods for understanding physical systems by treating them as small modifications to exactly solvable systems.

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Why does perturbation theory work so well?

In perturbation theory, we introduce a small perturbation to the system. This perturbation is usually a small parameter that slightly modifies the Hamiltonian or the equations of motion. We assume tha …
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Preservation of exact equations of motion in time-dependent perturbation theory for the Hami...

From the Hamilton-Jacobi formalism the solution for the unperturbed hamiltonian $H_0$ has a generating function $S(q,\alpha,t)$ such that $$K_0 = H_0(q, \frac{\partial S}{\partial q},t) + \frac{\parti …
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