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Radial SE

Our SE for the radial motion of the two nuclei has the form
$\displaystyle \left[- \frac{\hbar^2}{2\mu} \left(\frac{\partial^2}{\partial r^2...
...U_\alpha(r)\right] R_{\alpha;Kv}(r) = \varepsilon_{\alpha;Kv} R_{\alpha;Kv}(r).$     (1.26)

We therefore have two sets of quantum numbers \bgroup\color{col1}$ K$\egroup and \bgroup\color{col1}$ v$\egroup that describe the rotational and vibrational and state of the molecule for a given electronic state \bgroup\color{col1}$ \alpha$\egroup. Setting
$\displaystyle R_{\alpha;Kv}(r) = \frac{1}{r} P_{\alpha;Kv}(r)$     (1.27)

leads to a standard one-dimensional SE with a `proper' \bgroup\color{col1}$ \frac{d^2}{dr^2}$\egroup kinetic energy term,
$\displaystyle \left[ -\frac{1}{2\mu}\frac{d^2}{dr^2} + U_\alpha(r) + \frac{K(K+...
...ight] P_{\alpha;Kv}(r)
= \varepsilon_{\alpha;Kv}P_{\alpha;Kv}(r), \quad r\ge 0.$     (1.28)



Subsections

Tobias Brandes 2005-04-26