1. The problem statement, all variables and given/known data Calculate the mean square displacement x2 of the particle from its equilibrium position. 2. Relevant equations ∫ from -[itex]\infty[/itex] to +[itex]\infty[/itex] of Nv2 * Hv(y) * e-y^2 dy Since y=x/[itex]\alpha[/itex], [itex]\alpha[/itex]dy=dx yHv = vHv-1 + (1/2)Hv+1 3. The attempt at a solution https://www.dropbox.com/s/uiqbgzjjlqnnqwk/2014-02-14%2022.23.41.jpg What is boxed is where I distributed everything. That looked horrible so I applied the recursion relation once. I believe the last integral goes to zero. Integrating an odd function over a symmetrical range would be zero. But then everything would be zero and that's just wrong. There should be a relationship between v and m and kf and hbar from [itex]\alpha[/itex]. I apologize, but please explain the math as simple as possible. The math is the issue, not really the concept. EDIT: Should I apply the recursion relation once more in the integral as it has yHv?