It is always stated the quantum operators for **p** and E are the ones we´re familiar with (the operator for energy, $H=i\hbar\frac{\partial}{\partial t}$  and the momentum operator, $\mathbf{p}=-i\hbar\nabla $. But where do these operators come from? I understand that substitution of these operators in the classical momentum-energy relation amounts to the appearance of the Schrödinger equation (or the Klein-Gordon equation in the non-relativistic case, were, by the way, the E and **p** operators stay the same). But in the time of the development of quantum mechanics nobody knew the form of the right equation, so why replace the **p** and E by their now well known operator-form? Was is guessing, trial and error, or some other way to find the Schrödinger- (or Klein-Gordon-) equation? Were there all kinds of combinations of operators, $i$ and the the Planck-constant tried until the right one was found and fitted the data?