I want to compute the expectation value of the energy $ \langle H \rangle $ for a quantum system with the wave function $ \psi(x) $. This is done with $$ \langle H \rangle = \int_{-\infty}^{\infty} \psi^* \hat{H} \psi d x $$ where $$ \hat{H} = - \frac{\hbar^2}{2 m} \frac{d^2}{d x^2} + V(x) $$ is the Hamiltonian operator for some potential $V(x)$. How do I express $ \frac{d}{d x} $ in sage if I don't know on which function it will be applied?
I know it is possible to use psi.diff(x), but is there a way to declare the operator so that it automatically does the derivative when it is multiplied with some function?
