I apologize in advance for not being familiar with LaTex. 1. The problem statement, all variables and given/known data One thousand neutrons are in an infinite square well, with walls x=0 and x=L. The state of the particle at t=0 is : ψ(x,0)=Ax(x-L) How many particles are in the interval (0,L/2) at t=3? How many particles have energy E5 at t=3s? (That is the <E> at t=3s) 2. Relevant equations Wavefunction of the infinite square well: ψ(x)=Sqrt[2/L]Sin[n*Pi*x/L] Time dependence of wavefunctions: ψ(x,t)=∑cnψn(x,t) cn coefficients: cn=∫ψn(x)*f(x)dx 3. The attempt at a solution This problem is quite similar to this one: https://www.physicsforums.com/threads/neutrons-in-a-one-dimensional-box.242003/, except that now, one must calculate the quantities at a later time, forcing us to construct the full time-dependent solution (I suspect). I begin by normalizing the initial wavefunction, where I get: A=Sqrt[30/L2]. Then, in principle, we can get ψ(x,t) by calculating those cn coefficients, and plug it in the general solution (Griffiths example 2.2 does this). Well, this is all very nice and beautiful, but let's not forget what the question asks: calculating a probability at a later time. When putting this in Born's postulate to find the probability, the time dependence (a complex exponential) cancels out, so we don't even have to opportunity to 'plug in 3s! Not to mention, the infinite summation would also give me trouble when trying to perform the integral. (I hope I made sense...) So, does anyone have any advice on how else to attack this problem? Thank you!