> Complex numbers! I didn't expect complex numbers to have a deeper relation to quantum mechanics. Can you elaborate more on what you mean? Why are complex nu

> Complex numbers! I didn't expect complex numbers to have a deeper relation to quantum mechanics. Can you elaborate more on what you mean? Why are complex numbers “unexpected”? So much of contemporary physics is about distillation. You care more about things like consistency and simplicity over readability. Our current methods of solving these equations, vector calculus, requires certain operations, specifically, square roots and derivatives. To be able to utilize the well studied methods of linear algebra we need to make ample use of the Pythagorean theorem that ultimately uses a square root. To ensure that our model works in all domains we have to use a form of the square root that allows negative numbers. Complex numbers. It’s why we use e^(iHt/h_bar) in the Schrödinger equation. Rather than see it as “nature works by using exponentiation!” I see it as “exponentiation is ‘stable’ in the face of complex derivatives”, ie the derivative of the exponential function is the exponential function f(x)=e^x == f’(x)=e^x. So this formulation simplifies our calculations. These things can be calculated with any coordinate and numbering system, the ones we choose just help make the problems more tractable for us.