Time-Dependent Perturbation Theory

When the perturbation itself depends on time, we need a different toolkit — one built around transition rates between states.

Time Dependent Perturbation Theory

Content coming soon.

We use Fermi's golden rule to calculate the probability per unit time of a quantum system changing from one state to a continuous group of states.

W_{i \rightarrow[n]} = \frac{2 \pi}{\hbar} = \overline{|V_{ni}|^2} \rho(E_n)_{E_n \approx E_i}

which we can also write as

W_{i \rightarrow n} = \biggr(\frac{2\pi}{\hbar} \biggr) |V_{ni}|^2 \delta(E_n - E_i)

Content coming soon.

Content coming soon.

Fermi's Golden Rule gives the transition rate into a continuum of final states
The rate is proportional to $|V_{ni}|^2$ and the density of final states $\rho(E_n)$
Energy is conserved on average via the delta function $\delta(E_n - E_i)$