In
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
, a state space is an abstract
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consi ...
in which different "positions" represent, not literal locations, but rather
states of some physical system. This makes it a type of
phase space
In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usuall ...
.
Specifically, in
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
a state space is a
complex Hilbert space
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...
in which the possible instantaneous
?_.html" ;"title="Help:Find_sources.html" ;"title="Help:Find sources">? ">Help:Find_sources.html" ;"title="Help:Find sources">? states of the system may be described by unit vectors. These quantum state, state vectors, using Paul Dirac, Dirac's bra–ket notation, can often be treated like coordinate vectors and operated on using the rules of linear algebra. This
Dirac formalism of quantum mechanics can replace calculation of complicated
integrals
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with d ...
with simpler vector operations.
See also
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Configuration space (physics)
In classical mechanics, the parameters that define the configuration of a system are called '' generalized coordinates,'' and the space defined by these coordinates is called the configuration space of the physical system. It is often the case ...
for the space of possible positions that a physical system may attain
*
Configuration space (mathematics) for the space of positions of particles in a topological space
*
State space (controls)
In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables wh ...
for information about state space in control engineering
*
State space
A state space is the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory.
For instance, the to ...
for information about discrete state space in computer science
Notes
References
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Concepts in physics
Hilbert space
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