1. The problem statement, all variables and given/known data Say there exists a delta potential V(x) = α(x-L). Solve the eigenvalue problem to yield the energy eigenstates. Say a quanton is in an initial state given by Ψ(x)=Aeikox at t=0. What is Ψ(x,t)? 2. Relevant equations Schrodinger Eqn. 3. The attempt at a solution I solved the first part to find the energy eigenvectors (not-normalized), after applying the boundary condition (including the discontinuity at x-L), to get: Ψk(x) = A(eikx + B/A(e-ikx) x<L Ψk(x)=A(C/A)(eikx) x>L B/A and C/A were obtained from the boundary conditions, and of course represent the reflection and transmission coefficients, respectively. Since ψ(x,t) = ∫Ψk(x)⋅φ(k)dk where φ(k) represents the coefficients of the wave function, obtained via Fourier Transform. i.e. φ(k) = ∫Ψk*(x)⋅Ψ(x)dx I'm having trouble, qualitatively, understanding how to compute the given integral given that the initial state has a well-defined momentum and is travelling from the left to the right; would the integral with B/A(-ikx) vanish since it represents a left moving quanton, which is orthogonal to the right moving quanton in the initial state?