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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 the Schrodinger equation, around 1926. Other contributions were from [[Werner Heisenberg]], [[Niels Bohr]], [[John von Neumann]], and [[Hermann Weyl]].

Quantum mechanics consists of the breakthrough in [[physics]] in the 1920s in understanding how particles behave inside [[atom]]s.  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.

Quantum mechanics posits that an electron (or any other sub-atomic particle) behaves as both a wave and a particle.  As a result of the wave nature of the electron, the position of the electron can never be precisely known.  Whenever it is attempted to be measured, 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 posits that an electron (or any other sub-atomic particle) behaves as both a wave and a particle.  As a result of the wave nature of the electron, the position of the electron can never be precisely known.  Whenever it is attempted to be measured, 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.

Quantum mechanics forms the basis for our understanding of chemical reactions, as well as all computers and electronic devices today.

An important aspect of Quantum Mechanics is the predictions it makes about the radioactive decay of isotopes.  Radioactive decay processes, controlled by the wave equations, are random events.  A radioactive atom has a certain probability of decaying per unit time.  As a result, the decay results in an exponential decrease in the amount of isotope remaining in a given sample as a function of time.  The characteristic time required for 1/2 of the original amount of isotope to decay is known as the "half-life" and can vary from quadrillionths of a second (⁹B) to quintillions of years (¹⁸⁶W).

An important aspect of Quantum Mechanics is the predictions it makes about the [[radioactive decay]] of [[isotopes]].  Radioactive decay processes, controlled by the wave equations, are random events.  A radioactive atom has a certain probability of decaying per unit time.  As a result, the decay results in an exponential decrease in the amount of isotope remaining in a given sample as a function of time.  The characteristic time required for 1/2 of the original amount of isotope to decay is known as the "half-life" and can vary from quadrillionths of a second (⁹B) to quintillions of years (¹⁸⁶W).

==Mathematics==

==Mathematics==