1. The problem statement, all variables and given/known data Consider an electron subject to the following 1-D potential: [tex] U(x) = -U_0 \left( \delta(x+a) + \delta(x-a) \right) [/tex] where U_0 and a are positive reals. (a) Find the ground state of the system, its normalized spatial wavefunction and the parameter κ related to the ground state energy. (b) Write the transcendental equation satisfied by κ. Ok, so I'm a bit confused first by what κ is here. This was from an old qual and I don't quite remember the exact phrasing, and it is possible that my memory has failed me and that k (the wavevector?) was meant here instead of kappa. In any event, I don't quite see what kind of transcendental equation it is supposed to satisfy, exept perhaps by matching the three spatial wavefunction and their first derivative at x=-a and x=a? How would go about solving the Schrodinger equation with a potential given with delta functions? Any help would be appreciated.