The mathematical formulations of quantum mechanics are those
mathematical formalisms that permit a rigorous description of
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, q ...
. This mathematical formalism uses mainly a part of
functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined ...
, especially
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 natu ...
s, which are a kind of
linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early
1900s The 1900s may refer to:
* 1900s (decade), the decade from 1900 to 1909
* The century from 1900 to 1999, almost synonymous with the 20th century
The 20th (twentieth) century began on
January 1, 1901 ( MCMI), and ended on December 31, 2000 ( MM ...
by the use of abstract mathematical structures, such as infinite-dimensional
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 natu ...
s (
''L''2 space mainly), and
operators
Operator may refer to:
Mathematics
* A symbol indicating a mathematical operation
* Logical operator or logical connective in mathematical logic
*