A time-dependent logarithmic perturbation theory is developed that preserves closed-integral correction expressions and recovers exact results for the driven harmonic oscillator while providing accurate observables for the driven hydrogen atom.
However, we can resort to the PDE (II.9), rewritten in hybrid coordinates, which defines the corrections and solve it by either numerical or analytical means
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Time-Dependent Logarithmic Perturbation Theory for Quantum Dynamics: Formulation and Applications
A time-dependent logarithmic perturbation theory is developed that preserves closed-integral correction expressions and recovers exact results for the driven harmonic oscillator while providing accurate observables for the driven hydrogen atom.