1. The problem statement, all variables and given/known data (a) For the delta-function potential and with P<<1, find at k=0 the energy of the lowest energy band. (This is part A of Charles Kittel Solid State Physics problem 7.3) 2. Relevant equations (P/Ka)sin(Ka)+cos(Ka)=cos(ka) (note, K and k are different variables) ε=[itex]\hbar [/itex]2K2/(2m) 3. The attempt at a solution I have tried two different things. attempt 1) simply say (P/Ka)=0 so we get cos(Ka)=cos(0)=1 or K=arcos(1)/a plugging into energy equation ε=[itex]\hbar [/itex]2(arcos(1)/a)2/(2m)=0 which is obviously wrong second attempt is to Taylor expand the trig functions, and assume the because P<<1, Ka<<1, (in order to keep both left hand terms) and so (P/Ka)=1 after expanding and cancelling, 2cos(0)=1 which again stumps me I'm not sure what to do. I have the sln manual, which says to expand the first equation, to find P≈(1/2)(Ka)2 Thank you for any help.