Changes

==History==

==History==

Until the early 1900's, scientists believed that [[electron]]s and [[proton]]s were small discrete lumps.  Thus, electrons would orbit the nucleus of an [[atom]] just as planets orbit the sun. The problem with this idea was that, according to classical [[electromagnetism]], the orbiting electron would emit energy as it orbited.  This would cause it to lose rotational kinetic energy and orbit closer and closer to the proton, until it collapses into the proton!  Since atoms are stable, this model could not be correct.

Until the early 1900s, scientists believed that [[electron]]s and [[proton]]s were small discrete lumps.  Thus, electrons would orbit the nucleus of an [[atom]] just as planets orbit the sun. The problem with this idea was that, according to classical [[electromagnetism]], the orbiting electron would emit energy as it orbited.  This would cause it to lose rotational kinetic energy and orbit closer and closer to the proton, until it collapses into the proton!  Since atoms are stable, this model could not be correct.

The idea of "quanta", or discrete units, of energy was proposed by [[Max Planck]] in 1900, to explain the energy spectrum of [[black body]] radiation.  He proposed that the energy of what we now call a photon is proportional to its frequency. In 1905, [[Albert Einstein]] also suggested that light is composed of discrete packets (''[[quanta]]'') in order to explain the [[photoelectric effect]].

The idea of "quanta", or discrete units, of energy was proposed by [[Max Planck]] in 1900, to explain the energy spectrum of [[black body]] radiation.  He proposed that the energy of what we now call a photon is proportional to its frequency. In 1905, [[Albert Einstein]] also suggested that light is composed of discrete packets (''[[quanta]]'') in order to explain the [[photoelectric effect]].

In quantum mechanics, it is meaningless to make absolute statements such as "the particle is here". This is a consequence of the Heisenberg Uncertainty Principle which (simply put) states, "particles move," in an apparently random manner. Thus, giving a definite position to a particle is meaningless. Instead, scientists use the particle's "position function," or "wave function," which gives the probability of a particle being at any point.  As the function increases, the probability of finding the particle in that location increases. In the diagram, where the particle is free to move in 1 direction, we see that there is a region (close to the y-axis) where the particle is more likely to be found.  However, we also notice that the wave function does not reach zero as it moves towards infinity in both directions. This means that there is a high likelihood of finding the particle around the center, but there is still a possibility that, if measured, the particle will be a long ways away.

In quantum mechanics, it is meaningless to make absolute statements such as "the particle is here". This is a consequence of the Heisenberg Uncertainty Principle which (simply put) states, "particles move," in an apparently random manner. Thus, giving a definite position to a particle is meaningless. Instead, scientists use the particle's "position function," or "wave function," which gives the probability of a particle being at any point.  As the function increases, the probability of finding the particle in that location increases. In the diagram, where the particle is free to move in 1 direction, we see that there is a region (close to the y-axis) where the particle is more likely to be found.  However, we also notice that the wave function does not reach zero as it moves towards infinity in both directions. This means that there is a high likelihood of finding the particle around the center, but there is still a possibility that, if measured, the particle will be a long ways away.

When the particle is actually observed to be in a specific location, its wave function is said to have "collapsed". This means that if it is again observed immediately the probability that it will be found near the original location is almost 1. However, if it is not immediately observed, the wave function reverts back to its original shape as expected. The collapsed wave function has a much narrower and sharper peak than the original wave function.

When the particle is actually observed to be in a specific location, its wave function is said to have "collapsed". This means that if it is again observed immediately the probability that it will be found near the original location is almost 1. However, if it is not immediately observed, the wave function reverts to its original shape as expected. The collapsed wave function has a much narrower and sharper peak than the original wave function.

Collapsing of the wave function is by no means magic. In can be intuitively understood as this: You find a particle at a particular spot; if you look again immediately, it's still in the same spot.  

Collapsing of the wave function is by no means magic. In can be intuitively understood as this: You find a particle at a particular spot; if you look again immediately, it's still in the same spot.  

===The uncertainty principle===

===The uncertainty principle===

As a result of the wave nature of a particle, neither position nor [[momentum]] of a particle can never be precisely known.  Whenever its position is measured more accurately (beyond a certain limit), its momentum becomes less certain, and visa versa.  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]]:<ref>http://hyperphysics.phy-astr.gsu.edu/Hbase/uncer.html</ref>

As a result of the wave nature of a particle, neither position nor [[momentum]] of a particle can never be precisely known.  Whenever its position is measured more accurately (beyond a certain limit), its momentum becomes less certain, and vice versa.  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]]:<ref>http://hyperphysics.phy-astr.gsu.edu/Hbase/uncer.html</ref>

:<math> Dx \times Dp \ge \frac{h}{4\pi}</math>

:<math> Dx \times Dp \ge \frac{h}{4\pi}</math>