Why don't an electron and proton 1cm apart attract and collide?

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Do you know the value of the amplitude of the wave at c/3?
Is it possible to detect and measure with instruments the length and the amplitude of the wave of an electron?
Is that wave electromagnetic like light?
 
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The quantum wave is not electromagnetic; it is a probability amplitude ... it tells you how likely something is to be detected at each point in space. The probability for point X is |psi(X)|^2.

I do not know the probability amplitudes for the electrons in my system. But when you take an introductory QM course this type of calculation will be covered in one of the early lectures, or else will be a homework problem - it is one of the easiest as it represents the "free Hamiltonian": the only parameter is the momentum, hence only the kinetic energy appears in the Hamiltonian: H=p^2/2m.

You cannot directly measure the probability amplitudes, though it is possible to measure their effects when your experiment takes measurements: if the measurements are repeated you will see the probability distribution filled in. For example, I could see the probability distribution predicted by the electron diffraction process fill in, point by point on my imaging system.