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Physics LibreTexts

12: Time-Dependent Perturbation Theory

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Consider a system whose Hamiltonian can be written H(t)=H0+H1(t). Here, H0 is again a simple time-independent Hamiltonian whose eigenvalues and eigenstates are known exactly. However, H1 now represents a small time-dependent external perturbation. Let the eigenstates of H0 take the form H0ψm=Emψm. We know (see Section [sstat]) that if the system is in one of these eigenstates then, in the absence of an external perturbation, it remains in this state for ever. However, the presence of a small time-dependent perturbation can, in principle, give rise to a finite probability that if the system is initially in some eigenstate ψn of the unperturbed Hamiltonian then it is found in some other eigenstate at a subsequent time (because ψn is no longer an exact eigenstate of the total Hamiltonian). In other words, a time-dependent perturbation allows the system to make transitions between its unperturbed energy eigenstates. Let us investigate such transitions.

Contributors and Attributions

  • Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)


This page titled 12: Time-Dependent Perturbation Theory is shared under a not declared license and was authored, remixed, and/or curated by Richard Fitzpatrick.

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