I don't see how one can interpret the first paragraph as referring to the Schroedinger equation: "The first way -- which for most physicists today is still the

I don't see how one can interpret the first paragraph as referring to the Schroedinger equation: "The first way -- which for most physicists today is still the only way -- follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then you learn about the "blackbody paradox" and various strange experimental results, and the great crisis these things posed for physics. Next you learn a complicated patchwork of ideas that physicists invented between 1900 and 1926 to try to make the crisis go away. Then, if you're lucky, after years of study you finally get around to the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes that can be positive, negative, or even complex." It's hardly possible to even write the Schroedinger's equation on the blackboard without revealing the "central conceptual point" that complex numbers are involved. The "grueling differential equations" phrase refers to classical mechanics and electrodynamics. This part is actually true, you typically learn some classical mechanics and electrodynamics before you start QM.