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- Mathematical_formulation_of_quantum_mechanics abstract "The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. Such are 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 are 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.These formulations of quantum mechanics continue 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. While the mathematics permits calculation of many quantities that can be measured experimentally, there is a definite theoretical limit to values that can be simultaneously measured. This limitation was first elucidated by Heisenberg through a thought experiment, and is represented mathematically in the new formalism by the non-commutativity of operators representing quantum observables.Prior to the emergence of quantum mechanics as a separate theory, the mathematics used in physics consisted mainly of formal mathematical analysis, beginning with calculus, and increasing in complexity up to differential geometry and partial differential equations. Probability theory was used in statistical mechanics. Geometric intuition played a strong role in the first two and, accordingly, theories of relativity were formulated entirely in terms of geometric concepts. The phenomenology of quantum physics arose roughly between 1895 and 1915, and for the 10 to 15 years before the emergence of quantum theory (around 1925) physicists continued to think of quantum theory within the confines of what is now called classical physics, and in particular within the same mathematical structures. The most sophisticated example of this is the Sommerfeld–Wilson–Ishiwara quantization rule, which was formulated entirely on the classical phase space.".
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- Mathematical_formulation_of_quantum_mechanics title "Dirac picture".
- Mathematical_formulation_of_quantum_mechanics title "Heisenberg picture".
- Mathematical_formulation_of_quantum_mechanics subject Category:History_of_physics.
- Mathematical_formulation_of_quantum_mechanics subject Category:Quantum_mechanics.
- Mathematical_formulation_of_quantum_mechanics comment "The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. Such are 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.".
- Mathematical_formulation_of_quantum_mechanics label "Fundamentos matemáticos da mecânica quântica".
- Mathematical_formulation_of_quantum_mechanics label "Mathematical formulation of quantum mechanics".
- Mathematical_formulation_of_quantum_mechanics label "Mathematische Struktur der Quantenmechanik".
- Mathematical_formulation_of_quantum_mechanics label "Postulados de la mecánica cuántica".
- Mathematical_formulation_of_quantum_mechanics label "Postulati della meccanica quantistica".
- Mathematical_formulation_of_quantum_mechanics label "Postulats de la mécanique quantique".
- Mathematical_formulation_of_quantum_mechanics label "Postulaty mechaniki kwantowej".
- Mathematical_formulation_of_quantum_mechanics label "Wiskundige structuur van de kwantummechanica".
- Mathematical_formulation_of_quantum_mechanics label "Математические основы квантовой механики".
- Mathematical_formulation_of_quantum_mechanics label "صياغة رياضية لميكانيكا الكم".
- Mathematical_formulation_of_quantum_mechanics label "量子力学の数学的基礎".
- Mathematical_formulation_of_quantum_mechanics label "量子力學的數學表述".
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- Mathematical_formulation_of_quantum_mechanics sameAs 量子力学の数学的基礎.
- Mathematical_formulation_of_quantum_mechanics sameAs 양자역학의_수학적_공식화.
- Mathematical_formulation_of_quantum_mechanics sameAs Wiskundige_structuur_van_de_kwantummechanica.
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