$$E_n^1 \ = \ \langle \psi_n^0 | H' | \psi_n^0 \rangle$$įor the case of the quantum harmonic oscillator, our unperturbed energy eigenstates are given as the set $|n^0\rangle$. We first have to show that that there is no first-order correction to the energy. We then turn on a weak electric field (emphasis of weak, so the perturbation that we will introduce is sufficiently small).Īnyways, this means that our perturbation given as $H' \ = \ -qEx$ (our potential energy is shifted by this quantity). We are asked to consider a charged particle in the one-dimenssional quantum harmonic oscillator. Schroeter, Introduction to Quantum Mechanics, Third Edition, Cambridge University. Griffiths Quantum Mechanics 2nd Edition: Problem 6.5
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