The obvious fact that the eigenfunctions $\psi(\lambda)$ of the Hamiltonian $H(\lambda)=H_0+\lambda V$ are determined up to a phase factor $\exp\big(i\alpha(\lambda)\big)$ can be used to exhibit a simple method to find the correction $\epsilon_n$ of order $n$ to a non-degenerate energy level. Rules are given to write down all the terms which build up $\epsilon_n$ in terms of $\epsilon_k,\,k\leq n-2$, and series of matrix elements of the perturbation $V$.
A simple iterative method to write the terms of any order of perturbation theory in quantum mechanics
BRACCI, LUCIANO;PICASSO, LUIGI ETTORE
2012-01-01
Abstract
The obvious fact that the eigenfunctions $\psi(\lambda)$ of the Hamiltonian $H(\lambda)=H_0+\lambda V$ are determined up to a phase factor $\exp\big(i\alpha(\lambda)\big)$ can be used to exhibit a simple method to find the correction $\epsilon_n$ of order $n$ to a non-degenerate energy level. Rules are given to write down all the terms which build up $\epsilon_n$ in terms of $\epsilon_k,\,k\leq n-2$, and series of matrix elements of the perturbation $V$.File in questo prodotto:
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