That's brilliant, it's pretty much the exact question I had! Unfortunately there doesn't seem to be an answer in the book? It just sort of states the problem...
I'm not sure, this is all the question gives me. I think the question is somewhat open-ended. This is the reason I suspected there was some sort of "simple" reasoning behind the answer. Is there a method of writing out the wavelengths in a general way?
Homework Statement
Three particles, each of mass m, reside in a 1D "box" of length L. Find a complete set of wavefunctions,\phi_{k}(x) for the system. In this sense, "complete" means that any state of the system,\psi(x) can be written as a superposition of the wavefunctions...