Introduction to Quantum Mechanics · Problem 10.16

Scattering — David J. Griffiths

Physics — Quantum Mechanics · greens-function-one-dimensional

Problem

Find the Green's function for the one-dimensional Schrödinger equation, and use it to construct the integral form (analogous to Equation 10.66). Answer: ψ(x)=ψ0(x)−imℏ2k∫−∞∞eik∣x−x0∣V(x0)ψ(x0) dx0.(10.102)\psi(x) = \psi_0(x) - \frac{im}{\hbar^2 k}\int_{-\infty}^{\infty} e^{ik|x-x_0|}V(x_0)\psi(x_0)\,dx_0. \tag{10.102}

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