In Quantum Mechanics, we understand this
which satisfy a wave equation.
To compute the probability to find an electron at our thought experiment detector,
we add the probability amplitude to get to the detector through slit 1
to the amplitude to get to the detector through slit 2 and take the absolute square.
Quantum Mechanics completely changes our view of the world. Instead of a deterministic world, we now have only probabilities. We cannot even measure both the position and momentum of a particle (accurately) at the same time. Quantum Mechanics will require us to use the mathematics of operators, Fourier Transforms, vector spaces, and much more.
Jim Branson 2013-04-22