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A `Mini-Molecule': Perturbation Theory vs Non-Perturbative Bonding

At this stage, one usually discusses relativistic corrections to the Hydrogen spectrum which are calculated with perturbation theory. The degeneracy of a spectrum of a given Hamiltonian $\bgroup\color{col1}$ \hat{H}_0$\egroup$ can be lifted by additional perturbations $\bgroup\color{col1}$ \hat{H_1}$\egroup$ such that the spectrum of the perturbed Hamiltonian,

$\displaystyle {\color{col1}\hat{H}= \hat{H}_0+ \hat{H}_1},$

(2.1)

or at least parts of it, are no longer degenerate. This is all fine, but before doing so we have a critical look at perturbation theory and its limitations, using the simplest quantum mechanical system:

Subsections

Example: Two-Level System
- Exact solution
- Second Order Perturbation Theory

Tobias Brandes 2005-04-26