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    • 9.6: The Photoelectric Effect in Hydrogen
      https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_(Fowler)/09%3A_Perturbation_Theory/9.06%3A_The_Photoelectric_Effect_in_Hydrogen
      In the photoelectric effect, incoming light causes an atom to eject an electron. We consider the simplest possible scenario: that the atom is hydrogen in its ground state. The interesting question is:...In the photoelectric effect, incoming light causes an atom to eject an electron. We consider the simplest possible scenario: that the atom is hydrogen in its ground state. The interesting question is: for an ingoing light wave of definite frequency and amplitude, what is the probability of ionization of a hydrogen atom in a given time? In other words, assuming we can use time-dependent perturbation theory, what is the ionization rate?
    • 5.4: The Electron-Photon Interaction
      https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/05%3A_Quantum_Electrodynamics/5.04%3A_The_Electron-Photon_Interaction
      Now, we replace it by the vector potential operator derived in Section 5.3: \[\hat{\mathbf{A}}(\hat{\mathbf{r}},t) = \begin{cases} \displaystyle \sum_{\mathbf{k}\lambda} \sqrt{\frac{\hbar}{2\epsilon_0...Now, we replace it by the vector potential operator derived in Section 5.3: \[\hat{\mathbf{A}}(\hat{\mathbf{r}},t) = \begin{cases} \displaystyle \sum_{\mathbf{k}\lambda} \sqrt{\frac{\hbar}{2\epsilon_0\omega_{\mathbf{k}}V}}\, \Big(\hat{a}_{\mathbf{k}\lambda} \, e^{i(\mathbf{k}\cdot\mathbf{r} - \omega_{\mathbf{k}} t)} + \mathrm{h.c.}\Big)\, \mathbf{e}_{\mathbf{k}\lambda}, & (\mathrm{finite}\;\mathrm{volume}) \\ \displaystyle \int d^3k \sum_{\lambda} \sqrt{\frac{\hbar}{16\pi^3\epsilon_0\omega_{\ma…

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