Autocorrelation function and total absorption spectrum

In Section 2.5 we have constructed the degenerate continuum wavefunc-tions 4/ f(R, r Ef, n), which describe the dissociation of the ABC complex into A+BC(n). They solve the time-independent Schrodinger equation for fixed energy Ef subject to the boundary conditions (2.59). Furthermore, the 4/f(R,r Ef,n) are orthogonal and complete and thus they form a basis in the corresponding Hilbert space, i.e., any function can be represented as a linear combination of them. 

A wavepacket is nothing other than a coherent superposition of stationary states, each being multiplied by the time-evolution factor In the present case, a most general time-dependent wavepacket is con- 

The next step is the essential one we fix the coefficients c(Ef,n) by imposing the initial condition 

Inserting the right-hand side of (4.3) for t = 0 into (4.4) and using the orthogonality of the basis functions f(Ef,n) yields the relation 

Multiplying (4.3) from the left by 4 /(0) and integrating over all nuclear coordinates gives 

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