Glimpses of the quantal algebra in early papers on quantum mechanics

A closer reading of early papers on quantum mechanics reveals that the quantal algebra lies hidden beneath the surface. We will show from the standpoint of the quantal algebra that, in essence, Heisenberg came across the symmetric product of the quantal algebra in his remarkable 1925 paper, Born and Jordan limited a general Hamiltonian function to a linear form of the terms containing the symmetric product of the quantal algebra, and Dirac found that the most general operation d/dv is the Leibnitz identity of the quantal algebra.