Hey guys, this is my first post so go easy on me. I was looking over the simple case of a 1D particle restrained inside an infinite square well potential ("particle in a box") and was having some difficulty understanding the relationship between the energy states and the expectation value for the energy. Using the time independent Schrödinger equation and normalizing the wave function I get: ψ(x) = sqrt(2/L) * sin (n*pi*x / L) Which implies: k = n*pi / L = p / hbar = sqrt(2mE) / hbar E = (n*pi*hbar)^2 / 2m*L^2 Then I try calculating the expectation value for the energy. (Here is where I have trouble.) <E> = ∫ψ* i hbar ∂ψ/∂t dx = i hbar ∫ψ* 0 dx = 0 [Where the bounds of the integral are from -∞ to ∞] How can both of these statements about the energy of the particle be true? I feel like I am missing something fundamental. Does the uncertainty principle play a role here? Or is the Energy operator simply not valid in the time independent case of Schrödinger's equation?