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# Questions tagged [perturbation-theory]

A mathematical method to provide an approximate solution of complex problems as perturbation(deviation) of the known solution of a more simple problem. It is used mainly in quantum physics, but is not limited to it.

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### How can one obtain the same-spin and opposite-spin terms of the MP2 energy by integrating out the spin?

Just as specified on the psi4 website here: https://psicode.org/psi4manual/master/dfmp2.html, the Moller-Plesset Perturbation Theory states that the second order correction to the ground state energy, ...
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### Can the electronic configurations give any information about the actual structure of the atom?

The zeroth order wavefunction for an He atom in the ground state is $\psi^0_\text{He}=\psi_{1s}(1)\psi_{1s}(2)$ and hence the electronic configuration $1s^2$. But then we start making purterbations, ...
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### Is the correct zeroth-order wave function $\phi^{(0)}$ an eigenfunction of the perturbation Hamiltonian $H'$?

Consider the perturbation treatment of He $1s2s$ excited state configuration. The quantum mechanical Hamiltonian for the He-atom is: \begin{aligned} \hat{H} = \sum_{i=1}^2 h_i + \frac 1 {r_{1 2}} \\ ...
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### Proof for second-order perturbation term of energy

In perturbation theory, if \begin{align}{\hat {H}} &= {\hat {H}^{(0)}} + λ{\hat {H}^{(1)}} \tag{1}\\ {ψ} &= {ψ^{(0)}} + λ{ψ^{(1)}} +λ^2{ψ^{(2)}} + ... \tag{2}\\ {E} &= {E^{(0)}} + λ{E^{...
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