Quantum Mechanics
Introduction
Quantum Mechanics is a mathematical model developed to explain the behaviour of physics at very small scales. At these scales (roughly one trillion trillion trillionth of a centimetre) strange things start to happen - things that can't be explained by classical physical theories. Quantum Mechanics is a model that has proved extremely successful at predicting (if not necessarily explaining) these behaviours. [TODO: list some everyday phenomena that are only explainable via QM?]
Particles & Waves
The fundamental difference between Quantum Mechanics and classical physics is the concept of wave-particle duality. This is the idea that everything in the universe that we consider to be made of particles (all matter, effectively) is also representable as a wave. Everything in Quantum Mechanics follows from this idea. In classical physics, things are either particles (protons, neutrons, electrons, etc) or they are waves (sound, vibrations, etc). Waves are more abstract phenomena: they aren't actually made of anything - rather they move through mediums with no physical form of their own.
Particles are solid and definite. They bounce off each other, they take up space and pile up on one another. A bookshelf will fill up because the books in it each take up a portion of space and prevent any other particles from being in it.
Waves don't behave in the same manner. Waves will happily occupy exactly the same space - two sets of ripples on a lake will pass right through each other and carry on without seeming to notice. Instead of colliding, waves interfere. If two waves happen to peak at the same place at the same time, the resulting peak will be the height of the two individual peaks added together. This is a fundamental property of waves. If you started placing waves onto your bookshelf, they would move up and down the shelf, interfering with each other to form one combined wave that filled the entire shelf.
It's clear that particles and waves are very different from each other, so it seems impossible that they can represent the same thing. Yet a wide variety of experiments seemed to show contradictory results, some indicating that certain subatomic particles (electrons, photons) were, well, particles, some indicating that they were waves, displaying wave-like behaviour.
[TODO: summarise these experiments. Young's slits, Planck's solution to the Ultraviolet Catastrophe, the Photoelectric Effect, etc]
It has since been shown that even larger particles like atoms and molecules exhibit wave behaviour. Thus the unavoidable conclusion is that matter has wave-particle duality. It exists as both a particle and a wave, simultaneously.
[TODO: write more of this]
Wavefunctions and Probability Distributions
In Quantum Mechanics the measurable properties of an object (things like its position and momentum) are called observables. A key difference between Classical and Quantum Mechanics is that the values of observables are not necessarily known until they are measured. When measured, an observable can take any value in a range of values known as its spectrum. Whereas in Classical Mechanics you know an object is in a specific place, in Quantum Mechanics you can never be sure! A famous example of this is the Uncertainty Principle, which effectively requires that the combined uncertainty in the position and momentum of a particle cannot drop below a certain value. Thus as you confine a particle's position and measure it more precisely, the spectrum of possible values for its momentum widens.
See Also
- Some stuff.