1. The problem statement, all variables and given/known data Problem 13.7.17 in Mathematical Methods in Physical Sciences: Find the wavefunction of a particle in a cube, refering to 13.3.6. 0 < x < L, 0 < y < L, 0 < z < L 13.3.6: Find the wavefunction of a particle in a square 0 < x < L, 0 < y < L. Assume V = 0. 2. Relevant equations -(hbar)^2/2m * Laplacian(ψ) = i(hbar)*∂(ψ)/∂t 3. The attempt at a solution Use separation of variables. ψ = U(x,y,z)T(t) Substitute UT into the equation and then divide both sides by UT to separate it into time dependent and time independent parts. (hbar)^2/2m * Laplacian(U) - E*U = 0 i(hbar)*∂(ψ)/∂t = T Solve the time dependent ordinary differential equation for T: T = exp(-iEt/hbar) If the time independent schrodinger equation was in 1-D, it would be: -(hbar)^2/2m * ∂(U)/∂x = E*U Assume E = k^2, where k^2 = 2Em/(hbar)^2 ∂(U)/∂x = -k^2*U U must be a sin or cos function in terms of U(x) but due to boundary conditions that it must be 0 at x=0 and x=L, it cannot be cos which would be nonzero at x = 0. U = sin(kx), k = n∏/L where n = 1,2,3... By analog with the 1-D case, the 3-D solutions should be: Ux = sin k1 * x Uy = sin k2 * y Uz = sin k3 * z with the constants K being all a constant (n,m,p) times ∏/L . The final solution is then ψ = UxUyUzT = Ʃ A(nmp)sin(k1x)sin(k2y)sin(k3z)exp(-iEt/hbar) Now we attempt to use initial conditions to set up a triple Fourier series and find A(nmp) where the 1-D analog would be the Fourier series A(n) = (2/L) * ∫(initial condition functions) sin(kx)dx from 0 to L. The problem does NOT give initial conditions so I have no idea how to solve the problem now. What can I possibly assume for the initial conditions such that I can obtain a solution?