Approximate Methods - Approximate Methods The problems...

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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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Approximate Methods - Approximate Methods The problems...

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