I need some help beginning a problem set problem (just want hints, I'd like to figure it out myself).
The problem gives me the IR absorption for a diatomic, as well as the force constant for the bond. It asks me to identify the the average separation (bond length) of the two atoms.
I am stuck because the typical Schrodinger equation for harmonic oscillation takes "displacement from equilibrium length" as its variable: $\hat{H}\psi_{v}(x)=E_{v}\psi_{v}(x)$. A change of variables such as $x = l-l_{0}$ would require I know the average separation, which I am trying to solve for.
Any help or direction to relevant resources is greatly appreciated.