Quantum state space

In physics, a quantum state space is an abstract space in which different "positions" represent not literal locations, but rather quantum states of some physical system.

It is the quantum analog of the phase space of classical mechanics.

The dimension of this Hilbert space depends on the system we choose to describe.

In the formalism of quantum mechanics these state vectors are often written using Dirac's compact bra–ket notation.

The spin can be aligned with a measuring apparatus (arbitrarily called 'up') or oppositely ('down').

For example, a particle in one space dimension has one degree of freedom ranging from

[5]: 302 Even in the early days of quantum mechanics, the state space (or configurations as they were called at first) was understood to be essential for understanding simple quantum-mechanical problems.

In 1929, Nevill Mott showed that "tendency to picture the wave as existing in ordinary three dimensional space, whereas we are really dealing with wave functions in multispace" makes analysis of simple interaction problems more difficult.

The emission process is isotropic, a spherical wave in quantum mechanics, but the tracks observed are linear.

As Mott says, "it is a little difficult to picture how it is that an outgoing spherical wave can produce a straight track; we think intuitively that it should ionise atoms at random throughout space".

Mott then derives the straight track by considering correlations between the positions of the source and two representative atoms, showing that consecutive ionization results from just that state in which all three positions are co-linear.