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Approximate Methods
The problems discussed in the previous section (harmonic oscillator, rigid rotator,
etc.) are some of the few quantum mechanics problems which can be solved
analytically. For the vast majority of chemical applications, the Schrödinger equation
must be solved by approximate methods. The two primary approximation techniques
are the variational method and perturbation theory.
Perturbation Theory
The basic idea of perturbation theory is very simple: we split the Hamiltonian into a
piece we know how to solve (the ``reference'' or ``unperturbed'' Hamiltonian) and a
piece we don't know how to solve (the ``perturbation''). As long as the perburbation is
small compared to the unperturbed Hamiltonian, perturbation theory tells us how to
correct the solutions to the unperturbed problem to approximately account for the
influence of the perturbation. For example, perturbation theory can be used to
approximately solve an anharmonic oscillator problem with the Hamiltonian
(132
)
Here, since we know how to solve the harmonic oscillator problem (see
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 Fall '10
 LauraChoudry
 Chemistry

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