= Quantum quench
A <quantum quench> changes a <quantum system>'s control parameters rapidly and studies the subsequent <unitary time evolution>. In the ideal sudden limit, write an initial <energy eigenstate> $|m_i\rangle$ using a complete final <orthonormal eigenbasis>:
$$
|m_i\rangle=\sum_n c_n|n_f\rangle,\qquad c_n=\langle n_f|m_i\rangle,\qquad
|\psi(t)\rangle=\sum_n c_ne^{-iE_n^ft/\hbar}|n_f\rangle.
$$
The <Born rule> <probabilities> for a nondegenerate final <energy measurement> are $|c_n|^2$, with $\sum_n|c_n|^2=1$. For a degenerate <energy eigenvalue>, sum the <probabilities> over its orthonormal <energy eigenstates>. Subsequent relative <quantum phases> can alter other measurement <probabilities> even though these final <energy> populations stay fixed. A <quench> need not begin in an <energy eigenstate>; the same expansion applies to any initial <pure state>.
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