I'm kind of new to physical chemistry and trying to understand how, if at all, the correspondence principle (in the limit of large quantum numbers, quantum mechanics reproduces classical behavior of a system) relates to transition energies for electronic excitement in conjugated polyenes and quantum dots.

Our experiment used UV/vis spec to measure absorption and calculated theoretical values of energy with the particle in a box/sphere models. So why does the difference between experimental and theoretical energy get larger as length gets smaller?

Someone proposed the correspondence principle here, but I don't see how that has to do with going from the ground state (HOMO or valence band) state to the first excited state (LUMO or conduction band) that we're dealing with in the experiment. What am I not understanding here? Thank you!

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    $\begingroup$ I think that the agreement is pretty accidental. The particle in a box is a very crude model of a molecule but it does show basic trends, bigger box (i.e. more conjugation) gives lower energy levels with smaller gaps between them. Thats it; don't read any more into it than that and use it as a 'rule of thumb' sort of thing. $\endgroup$
    – porphyrin
    Oct 24, 2016 at 21:04