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Quantum mechanics consists of the breakthrough in physics in the 1920s in understanding how particles behave inside atoms.  Classical mechanics, as initially discovered by [[Isaac Newton]], cannot explain atomic behavior.  [[Erwin Schrodinger]] is generally credited with the formulation of quantum mechanics, around 1926, with contributions from [[Werner Heisenberg]] and [[Niels Bohr]].

Quantum mechanics consists of the breakthrough in physics in the 1920s in understanding how particles behave inside atoms.  Classical mechanics, as initially discovered by [[Isaac Newton]], cannot explain atomic behavior.  [[Erwin Schrodinger]] is generally credited with the formulation of the Schrodinger equation, around 1926. Other contributions were from [[Werner Heisenberg]], [[Niels Bohr]], [[John von Neumann]], and [[Hermann Weyl]].

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.

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.

==Mathematics==

==Mathematics==

The mathematics of Quantum mechanics can be formulated in a number of ways: the "matrix mechanics" of Werner Heisenberg, the "path integrals" of [[Richard Feynman]], or the "wave mechanics" of Erwin Schrodinger. Wave mechanics is the most common formulation. It uses the language of infinite dimensional [[Hilbert Space]]s; observables such as position and momentum are [[operator]]s on such Hilbert Spaces.

The mathematics of Quantum mechanics can be formulated in a number of ways: the "matrix mechanics" of Werner Heisenberg, the "path integrals" of [[Richard Feynman]], or the "wave mechanics" of Erwin Schrodinger. Wave mechanics is the most common formulation. It uses the language of infinite dimensional [[Hilbert Space]]s; observables such as position and momentum are [[operator]]s on such Hilbert Spaces.