Question

As I understand, Fermi resonances occur when two (nearly) resonant vibrational states—most commonly a fundamental and overtone or combination mode—that are of the same symmetry interact, which, in the usual way, causes mixing between the two states and an increase in the energy difference between the two (a Rabi splitting, essentially).

But it puzzles me that this is even possible if I assume that both of the two states that comprise the resonance are actually normal modes. The resonance/interaction relies on the matrix element between the two states, ⟨ψ1|H|ψ2⟩
, being nonzero. But by the definition of normal modes, these states should be eigenstates of H
and orthogonal, shouldn't they? Then the matrix element is necessarily zero, so is the resonance only possible in the presence of some additional perturbation or did I misunderstand something?

Answer 1

Fermi resonances can occur even if the states involved are normal modes due to perturbations or anharmonic effects.

Step-by-step explanation:

Fermi resonances occur when two (nearly) resonant vibrational states interact, causing mixing and an increase in the energy difference between the states. While it is true that normal modes are eigenstates of the system's Hamiltonian and should be orthogonal, Fermi resonances can still occur due to perturbations or anharmonic effects. These perturbations break the orthogonality condition, allowing for a non-zero matrix element between the two states, leading to resonance.