1. The problem statement, all variables and given/known data For a free particle, Given psi(x,0) = Aexp(-ax^2), find psi(x,t) 2. Relevant equations phi(k) = 1/(sqrt(2pi)) times integral from -inf to +inf (psi(x,0)exp(-ikx))dx psi(x,t) = 1/(sqrt(2pi)) times integral from -inf to +inf (phi(k)exp(i(kx - (hk^2)t/2m)))dk my apologies for the messy notation 3. The attempt at a solution I have normalized psi(x,0) to get A = (pi/a)^-1/4 and have my psi(k) = (1/(sqrt(2pi))) ((pi/a)^-1/4) times integral from -inf to +inf (exp(-ax^2) exp(-ikx)) dx. regrettably, my math is quite out of practice, and I am unsure how to proceed. the text says something about 'completing the square' which gives y = (sqrt(a))[x + (b/2a)], then ((ax^2) + bx) = (y^2) - (b^2)/4a. After this, integration by parts doesnt seem to help (or I'm missing something, which is quite likely). Any help is greatly appreciated!