Quantum mechanics and quantum field theories underlie modern fundamental physics, by providing the most low-level descriptions of the universe currently accepted by the scientific community.

Whilst quantum theory tends towards classical physics in the limit, so that classical theories provide a good approximation in most cases, there are crucial differences in the basic principles, and some significant differences in the predictions in small scale situations (and in some large scale situations, including superfluidity and superconductivity).

Differences to Classical Physics

The main differences between the quantum model and the classical model are as follows:

• It is a probabilistic theory. This means that many calculations using the system give the chance of the different outcomes rather than describing which event actually happens with certainty.
• There is an uncertainty relationship between conjugate variables. This means that after determining or measuring one variable (like position) to some accuracy, the value of the other variable (like momentum) has an uncertainty which is larger if the the first measurement is more accurate - so the variance (spread) of the second measurement is larger.
• It uses wave-particle duality. This means that both matter and radiation are thought of as behaving in wave-like ways and particle-like ways at the same time.
• Many quantities are quantized (hence the name). This means that they can only take certain, fixed values (often multiples of some constant).

Mathematical Theory

See Mathematical Formulation of Quantum Mechanics.

There are many (essentially equivalent) ways of formulating quantum mechanics, but the following approach is both representative and probably the clearest.

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Motivations and Evidence for QM

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Index

Quantum Physics

Topics in quantum mechanics and field theories