I'm studying Sakurai at the moment, time-dependent perturbation theory (TDPT). I'm having a problem in understanding a basic concept here.(adsbygoogle = window.adsbygoogle || []).push({});

According to Sakurai we have the following problem:

Let a system be described initially by a known hamiltonian H_{0}, being in one of its eigenstates |i>. Then, a time-dependent perturbation (V) is added to the system, with the total hamiltonian now being H=H_{0}+V. Now Sakurai asks, what is the probability of finding the system, at time t, in the energy eigenstate |n> of H_{0}.

Here is where my problem is.. We have a system being described by a hamiltonian H (the total hamiltonian), also being in an eigenstate of H at time t, and we want to know in which eigenstate ofanotherhamiltonian H_{0}the state of the system will collapse if we measure it! Can we do that? For example, if i have the electron of H_{1}at the ground state, am i able to expand this eigenstate to the basis ofanotherhamiltonian -like the one of a harmonic oscillator- and then say that im going to measure in which state (and in which energy) of the harmonic oscillator the electron of the hydrogen atom is going to be??

I must have been missing something very crucial here...

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# Time-dependent perturbation theory

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