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I know that Dirac was able to show that Heisenberg's and Schrodinger's formulations were equivalent to his own, but was Dirac's formulation (motion in Hilbert space) based on first principles like Newton's and Einstein's? Or are these formulations just mathematical that happen to match quantum phenomenon?

Either way, it was powerful stuff. I was just wondering what those first principles were. Doing a little research online, it seems like first principles for quantum mechanics are still a work in progress.