1. The problem statement, all variables and given/known data Consider a one-dimensional, nonrelativistic particle of mass m which can move in the three regions defined by points A, B, C, and D. The potential from A to B is zero; the potential from B to C is (10/m)(h/ΔL)2; and the potential from C to D is (1/10m)(h/ΔL)2. The distance from A to B is ΔL; the distance from B to C is 10ΔL; and the distance from C to D is chosen such that the ground state has the same probability between A and B as between C and D. Exploit the fact that this potential is very close to that of two independent infinite square wells to estimate the distance from C to D. 2. Relevant equations For an infinite square well with zero potential, En = h2n2/8ma2 (a being the width of the well), and ψn=√(2/a) sin(nπx/a) 3. The attempt at a solution It's been quite a while since I've needed to use my physics, so I'm pretty rusty, and I'm trying to start brushing up on it again before I start grad school. This one's kind of thrown me for a bit of a loop, maybe because the wording seems weird to me. From what I'm understanding, the probability that E1,AB is measured is equal to that the probability that E1,CD is measured. Based on this I've been trying to equate the expansion coefficient for the ground state ∫ψn*ψ dx for a particle in region AB and for a particle in region CD, but this approach has proven fruitless so far. Any thoughts on how to proceed, or am I completely misunderstanding this one?