quantum state

A quantum state is the complete description of a quantum system — everything the theory can possibly know about it at a given moment. From the state, and only from the state, you compute the probabilities of every conceivable measurement outcome. It can be expressed as a wavefunction, as an abstract state vector, or in still other ways, but all of these are different costumes for the same underlying physical situation.

What is striking is how spare this description is. Classically, knowing a particle's state means knowing its exact position and momentum together. In quantum mechanics the state already contains the maximum information nature allows, yet it generally cannot pin down position and momentum at once — the uncertainty relation is not a gap in the description but a feature of it. A complete quantum state can still leave the outcome of a measurement genuinely undetermined, fixing only the odds.

States come in two kinds worth distinguishing honestly. A pure state, describable by a single wavefunction, represents maximal knowledge. A mixed state describes a situation where we have only statistical information — a probabilistic blend of pure states — and is handled with a density matrix. The unqualified phrase 'quantum state' usually means the pure case, the fullest specification of an individual system that quantum mechanics permits.