Perturbation Theory - Physical Chemistry - Lecture Notes, Study notes of Physical Chemistry

Download Perturbation Theory - Physical Chemistry - Lecture Notes and more Study notes Physical Chemistry in PDF only on Docsity! Rayleigh-Schrödinger Perturbation Theory Begins with a solved quantum mechanical problem. Solve a new problem by defining a perturbation (or change) to the original problem. )()()()(ˆ o n o n o n o EH Ψ=Ψ solved "unperturbed" problem 'ˆˆˆ )( HHH o += Hamiltonian of real "perturbed" problem τdHEE on o n o nn )(*)()( 'ˆ Ψ∫ Ψ+= Energy of perturbed problem correct to first-order. There are expressions for higher-orders of perturbation theory, but these get progressively more complicated. For instance, the energy corrected to second-order requires the knowledge of the wavefunction corrected to first-order: Wavefunction Corrected to First-Order: ∑ − ∫ ΨΨ=Ψ ≠ij o j o i o i o j n EE dH )()( )(*)( )1( 'ˆ τ Energy Corrected to Second-Order: ττ dHdHEE n o n o n o n o nn )1(*)()(*)()( 'ˆ 'ˆ Ψ∫ Ψ+Ψ∫ Ψ+= Docsity.com