1. The problem statement, all variables and given/known data This integral has to do with the probability amplitude that a free particle at position x0 is found at x at some time t. With H = p2/(2m), this involves evaluating the integral 1/(2π)3∫d3p e-i(p2/(2m))t eip(x-x0) The answer is (m/(2πit))3/2e(im(x-x0)2)/(2t) 2. Relevant Equations H = p2/(2m) 3. The attempt at a solution I am not sure how to work with d3p, since I don't know how to decompose it in terms of p besides dpxdpydpz. When I try to evaluate that integral Mathematica takes forever, so I'm not sure its the right approach. When I just use this instead and evaluate from -∞ to ∞ or 0 to ∞ I get e(im(x-x0)2)/(2t) times a factor that does not equal (m/(2πit))3/2 and with some combinations of erf functions which is a red flag. How do I evaluate this?