Meaning of phase space | Babel Free

Definitions

1. Given a (dynamical) system, any topological space such that every point in the space's underlying set uniquely represents a state of the system and every possible state is represented by some point;
   countable, uncountable
2. Given a (dynamical) system, any topological space such that every point in the space's underlying set uniquely represents a state of the system and every possible state is represented by some point; (less formally) the underlying set of such a topological space.
   countable, uncountable
3. the underlying set of such a topological space.
   countable, uncountable

Examples

“For mechanical systems, the phase space usually consists of all possible values of position and momentum variables.”

“The phase space of a single material point is a manifold M×V*, and the Newton state-space is identifical^([sic]) with M×V.”

“2006, Matthew Charles Cargo, Phase Space Approaches to Higher Order WKB Approximations, University of California, Berkeley, page 8, Their energies are those of the level sets p²/2+V(x)=E that enclose an area of 2π hbar (n+1/2) in the classical phase space. Despite embracing a configuration space point of view, these methods have produced a phase space result.”

“The distribution of particles in phase space is given either by the injector characteristics and injection process or in the case of electron beams by the equilibrium of quantum excitation due to synchrotron radiation and damping.”

CEFR level