On the (Non)Equivalence of the Schrodinger and Heisenberg Pictures of Quantum Mechanics

The aim of this short Note is to show that the Schrodinger and Heisenberg pictures of quantum mechanics cannot be equivalent unless one uses a quantization rule clearly stated by Born and Jordan in their famous 1925 paper. This rule is sufficient and necessary to ensure energy conservation in Heisenberg's matrix mechanics. It follows, in particular, that Schrodinger and Heisenberg mechanics yield different theories if one quantizes the Hamiltonian using the Weyl prescription.