Quantum mechanics
Quantum mechanics consists of the breakthrough in physics in the 1920s in understanding how particles behave inside atoms. Classical mechanics, as discovered mostly by Isaac Newton, cannot explain atomic behavior.
Classical mechanics would predict that an electron orbits a proton just as planets orbit the sun. Classical electromagnetism would predict that the orbiting electron would emit a time-varying electrical field just as a radio station does. But the electron would lose energy as it emits this radiation, and would orbit closer and closer to the proton, until it collapses into the proton! Such a model cannot be correct.
Quantum mechanics discovered that an electron behaves as both a wave and a particle. As a result of the wave nature of the electron, the position of the electron is never precisely known. When it is observed, however, knowledge of the electron's velocity is lost. Hence, there is an inherent uncertainty that prevents precisely measuring both the position and the momentum simultaneously. This is known as the Heisenberg uncertainty principle.
Quantum mechanics forms the basis for our understanding of chemical reactions, as well as all computers and electronic devices today.
For an excellent discussion of quantum mechanics, see: http://www.chemistry.ohio-state.edu/betha/qm/
See also: Momentum (operator)