1. The problem statement, all variables and given/known data A particle is in a region with the potential V(x) = κ(x2-l2)2 What is the approximate ground state energy approximation for small oscillations about the location of the potential's stable equilibrium? 2. Relevant equations ground state harmonic oscillator ~ AeC*x2 3. The attempt at a solution My plan is to find the value of x for which V(x) is at stable equilibrium, then expand about that point, and the expansion should look something like the harmonic oscillator potential (1/2*mωx2). Once the potential is known, I know H = p2/2m + V, and I can use <0|H|0> to find the ground state energy, where |0> is the GS energy eigenstate for the harmonic oscillator. I have found that the stable equilibrium of V(x) is at x = l. Next, I expanded V(x) about this point and found: V = 4κl2(x2-2lx+l2) + O(x-l)3 But what can I do about the 2lx term? I need it to get lost in order to get the HO potential, right?