Hellmann-Feynman Theorem

The Hellmann-Feynman Theorem states that once a quantum system's wavefunction has been found for a Hamiltonian depending on some parameter, the derivative of the system's energy with respect to that parameter equals the expectation value of the derivative of the Hamiltonian itself, so that forces and other parameter derivatives can be computed directly from the wavefunction already found rather than by separately differentiating the energy. Named for Hans Hellmann and Richard Feynman, it is a standard computational tool of quantum chemistry and quantum mechanics.