I'm reading Modern Particle Physics by Mark Thomson and watching Susskind's lecture on QM. In Thompson's book, equation (2.41) the wavefunction is expressed in terms of complete set of states of the unperturbed Hamiltonian as(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \Psi(\textbf{x}, t) = \sum_{k} c_k(t)\phi_k(\textbf{x})e^{-iE_kt} [/tex]

Susskind explains the same thing and the result is

[tex] |\Psi(\textbf{x}, t)\rangle = \sum_{j} \alpha_j(0)e^{-iE_jt}|j\rangle [/tex]

Is it correct to change

[tex] \alpha_j(0) \rightarrow \alpha_j(t) [/tex]

and use

[tex] |\Psi(\textbf{x}, t)\rangle = \sum_{j} \alpha_j(t)e^{-iE_jt}|j\rangle [/tex]

in the presence of an interaction Hamiltonian?

After introducing time-dependent coefficients α_{j}, Susskind's and Thompson's expressions should be "equal", right?

Many thanks :)

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# I Fermi's golden rule derivation

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