written by Gina Passante, Paul J. Emigh, Tong Wan, and Peter S. Shaffer

We have investigated the extent to which students can qualitatively determine the effect of perturbations to a Hamiltonian on the energies of the eigenfunctions. The results indicate that after lecture instruction many students cannot determine some important features of the first-order correction. We examine the possibility that this failure may stem from a lack of understanding of the inner product.  Since perturbations are often represented graphically, the focus has been on student ability to determine the inner product of functions represented graphically. In the process, we have found that some students are unable to find inner products even in contexts outside of quantum mechanics.

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Last Modified December 16, 2015

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