Heisenberg's original differentiation trick was eventually extended to a full semiclassical derivation of the quantum condition, in collaboration with Born and Jordan. Once they were able to establish that i ℏ ℏ { X , P } P B ⟼ ⟼ [ X , P ] ≡ ≡ X P − − P X = i ℏ ℏ , this condition replaced and extended the old quantization rule, allowing the matrix elements of P and X for an arbitrary system to be determined simply from the form of the Hamiltonian.