  The aim of the famous Born and Jordan 1925 paper was to put Heisenberg's
matrix mechanics on a firm mathematical basis. Born and Jordan showed that if
one wants to ensure energy conservation in Heisenberg's theory it is necessary
and sufficient to quantize observables following a certain ordering rule. One
apparently unnoticed consequence of this fact is that Schr\"odinger's wave
mechanics cannot be equivalent to Heisenberg's more physically motivated matrix
mechanics unless its observables are quantized using this rule, and not the
more symmetric prescription proposed by Weyl in 1926, which has become the
standard procedure in quantum mechanics. This observation confirms the
superiority of Born-Jordan quantization, as already suggested by Kauffmann. We
also show how to explicitly determine the Born--Jordan quantization of
arbitrary classical variables, and discuss the conceptual advantages in using
this quantization scheme. We finally suggest that it might be possible to
determine the correct quantization scheme by using the results of weak
measurement experiments.
