Bad Qubits — Learn Quantum by Doing

Multiple choice

Time-independent perturbation theory is reliable when, for every state m that the perturbation couples to the state n, the ratio |<m|H'|n>| / |E_n - E_m| is much less than 1. Which situation makes the expansion FAIL even when the perturbation H' itself is tiny?

The unperturbed energies are all very large and positive
Two unperturbed levels are nearly degenerate, so the energy gap E_n - E_m approaches zero and the denominator blows up
The perturbation H' is exactly Hermitian
The unperturbed states are orthonormal