How Does Equation (92) Follow from Equation (91) in the Breit-Wigner Derivation?

[BOYLANATOR]

Homework Statement

The start of the derivation is shown in the attached image. I don't follow the argument that takes us from (91) to (92).

The Attempt at a Solution

I accept that the wavefunction of (91) is not an eigenstate of the Hamiltonian. I'm not clear where equation (92) came from though. Any comments that may offer an insight would be appreciated.

 

[invisiblefrog]

They're just using the fact that the set of functions $\left\{e^{ikt}\right\}$, where k may be any real number, forms an orthogonal basis, in terms of which any integrable function may be expressed. Same idea as a Fourier transform.