Mathematical Formulation of Quantum Mechanics
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High Quality Content by WIKIPEDIA articles! The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. It is distinguished from mathematical formalisms for theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces and operators on these spaces. Many of these structures were drawn from functional analysis, a research area within pure mathematics that was influenced in part by the needs of quantum mechanics. In brief, values of phy...
High Quality Content by WIKIPEDIA articles! The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. It is distinguished from mathematical formalisms for theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces and operators on these spaces. Many of these structures were drawn from functional analysis, a research area within pure mathematics that was influenced in part by the needs of quantum mechanics. In brief, values of physical observables such as energy and momentum were no longer considered as values of functions on phase space, but as eigenvalues (more precisely: as spectral values (point spectrum plus absolute continuous plus singular continuous spectrum)) of linear operators in Hilbert space. This formulation of quantum mechanics continues to be used today. At the heart of the description are ideas of quantum state and quantum observable which are radically different from those used in previous models of physical reality.
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