Alright, I'm in my first QM course right now, and one of the topics we've looked at is solving the one-dimensional time-independent Schrodinger equation for various potentials, such as the harmonic oscillators, infinite and finite square wells, free particles, and last, but not least, the dirac delta function potential. For each of these, with the exception of the dirac delta function, I can think of real-life situations that somewhat resemble these potentials. With the harmonic oscillator, we've got diatomic molecules. The potential wells are basically like containers. And free particles are obvious. (Well, these potentials are very rough ideas of what those real life situations would look like.) But when it comes to the dirac delta function potential, I don't know of any real life situations that resemble it, and thus I cannot figure out why it is important to study it. The book we're using (Griffiths) doesn't seem to explain this. I asked my professor about this, but as I sit here during spring break while trying to think about his response, I guess I didn't really understand it or was satisfied with it. Come to think of it, it was so loaded that I don't even remember what the response was at this point! So perhaps I could get some enlightenment on this issue here?