Physics Asked on July 31, 2021
I want to calculate the Frank-Condon Factors using the standard equation:
$$q_{v’v”}=left[int psi_{v’}^* psi_{v”} drright]^2$$
I have the vibrational wave functions of $v’$ and $v”$ in numeric form (i.e. points and not in analytical form). Now, if we take the complex conjugate of the vibrational wave function $v’$ and we multiply it with the vibrational wave function $v”$, we get a single value as an integrand.
My question is, how can we solve the integral in this case:
Is it a definite integral? If yes, then what are the lower and upper boundaries in this case? Are they the internuclear distances $r’_e$ and $r”_e$?
If not, and it is an indefinite integral, then we will get a single value multiplied by a variable, and thus not obtaining a value of the FCF which is between 0 and 1.
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