Time-Independent Perturbation Theory (Non-Degenerate)
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This content is primarily based on Section 8, “Approximation Method,” in Chapter 2 of Physics of Atoms and Molecules (2nd Edition) by B. H. Bransden and C. J. Joachain1.
Physics of Atoms and Molecules
B. H. Bransden and C. J. Joachain, Benjamin Cummings
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1. Summary
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We aim to solve the time-independent Schrödinger equation (TISE):
$$ \begin{align} (\hat{H}_0+\hat{H}’)\varphi = E \varphi \end{align} $$
Two-Level System with Periodic Perturbation
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This content is primarily based on Section 8, “Approximation Method,” of Chapter 2 in Physics of Atoms and Molecules (2nd Edition) by B. H. Bransden and C. J. Joachain1.
1. Problem Setup
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Consider the time-dependent Schrödinger Equation
$$ \begin{align} \label{e1} i\hbar \frac{\partial}{\partial t}|\Psi\rangle = \hat{H}(t)|\Psi\rangle \end{align} $$
where $\hat{H}$ is expressed using the unperturbed Hamiltonian $\hat{H}_0$ and the perturbed Hamiltonian $\hat{H}’(t)$ as follows: