## Tag Archives: schrodinger equation

This is a continuation of the previous post on Green’s Functions.

When you have a hammer, every problem looks like a nail.

Take the Schrodinger equation: $\hat{H} \psi(\vec{x},t) = i h \frac{\partial\psi(\vec{x},t)}{\partial t}$

Writing it as $(-\frac{h^2}{2 m}\nabla^2 - i h \frac{\partial}{\partial t}) \psi(\vec{x},t)=-V(\vec{x},t)\psi(\vec{x},t)$, we can try and come up with a green’s function for it.

What we’d like to be able to do is start with the wavefunction and potential at some point in time, and have it tell us the wavefunction for all times.

The standard QM thing to do would be to write the wavefunction as the sum of eigenstates of the Hamiltonian, them time evolve each of them. But instead, let’s see how far Mr. Green can take us.