You are spot on here: the heat equation and the Schrodinger equation are both special cases of the wave equation. A major difference between the two is that the Schrodinger equation deals with complex numbers, as you state. Transition between states is not instantaneous, though it is very fast, on the scale of attoseconds (10^-18 seconds).
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You are spot on here: the heat equation and the Schrodinger equation are both special cases of the wave equation. A major difference between the two is that the Schrodinger equation deals with complex numbers, as you state. Transition between states is not instantaneous, though it is very fast, on the scale of attoseconds (10^-18 seconds).