Changes

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 immediately 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 is never 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.  This decay is random, and the randomness is inherently a quantum mechanical effect.  

An important aspect of Quantum Mechanics is the predictions it makes about the radioactive decay of isotopes.  This decay is random, and the randomness is inherently a quantum mechanical effect.  As a result, the decay follows "1st-order kinetics" - typically resulting in an exponential decrease in the amount of isotope present 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 billionths of a second to billions of years.

==Mathematics==

==Mathematics==

The mathematics of Quantum mechanics can be formulated using the language of infinite dimensional [[Hilbert Space]]s; observables such as position and momentum are [[operator]]s on such Hilbert Spaces, or using alternatively using matrices.

The mathematics of Quantum mechanics is formulated using the language of infinite dimensional [[Hilbert Space]]s; observables such as position and momentum are [[operator]]s on such Hilbert Spaces.

==External Links==

==External Links==