In Quantum Mechanics, we understand this
**wave-particle duality**
using (complex)
probability amplitudes
which satisfy a wave equation.

The probability to find a particle at a position at some time is the absolute square of the probability amplitude .

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