View source for Physics:State space

In [[Physics:Physics|physics]], a '''state space''' is an abstract [[Space|space]] in which different "positions" represent, not literal locations, but rather states of some physical system. This makes it a type of [[Physics:Phase space|phase space]].

== Quantum Mechanics ==
Specifically, in [[Physics:Quantum mechanics|quantum mechanics]] a state space is a [[Complex number|complex]] [[Hilbert space]] in which each [[Unit vector|unit vector]] represents a different state that could come out of a measurement. Each [[Unit vector|unit vector]] specifies a different dimension, so the numbers of dimensions in this [[Hilbert space]] depends on the system we choose to describe.<ref>{{Cite book |last=McIntyre |first=David |title=Quantum Mechanics: A Paradigms Approach |publisher=Pearson |year=2012 |isbn=978-0321765796 |edition=1st}}</ref> Any state vector in this space can be written as a [[Linear combination|linear combination]] of unit vectors. Having an nonzero component along multiple dimensions is called a [[Physics:Quantum superposition|superposition]].  These [[Physics:Quantum state|state vectors]], using [[Biography:Paul Dirac|Dirac's]] [[Bra–ket notation|bra–ket notation]], can often be treated like [[Coordinate vector|coordinate vector]]s and operated on using the rules of [[Linear algebra|linear algebra]]. This [[Bra–ket notation|Dirac]] [[Physics:Mathematical formulation of quantum mechanics|formalism of quantum mechanics]] can replace calculation of complicated integrals with simpler vector operations.

==See also==
*[[Physics:Configuration space|Configuration space]] 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) for information about '''state space''' in control engineering
*[[State space]] for information about discrete state space in computer science

==Notes==
{{Reflist}}

==References==
*{{cite book | author=Claude Cohen-Tannoudji |title=Quantum Mechanics | publisher=John Wiley & Sons. Inc. |year=1977|isbn=0-471-16433-X}}
*{{cite book | author=David J. Griffiths | title=Introduction to Quantum Mechanics | publisher=Prentice Hall |year=1995|isbn=0-13-124405-1}}
*{{cite book | author=David H. McIntyre |year=2012 |title=Quantum Mechanics: A Paradigms Approach |publisher=Pearson |isbn=978-0321765796}}

[[Category:Concepts in physics]]
[[Category:Hilbert space]]



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