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강연자 지운식
소속 충북대학교
date 2011-04-14
We start with the famous Heisenberg uncertainty principle to give the idea of the probability in quantum mechanics. The Heisenberg uncertainty principle states by precise inequalities that the product of uncertainties of two physical quantities, such as momentum and position (operators), must be greater than certain (strictly positive) constant, which means that if we know one of the quantities more precisely, then we know the other one less precisely. Therefore, in quantum mechanics, predictions should be probabilistic, not deterministic, and then position and momentum should be considered as random variables to measure their probabilities.
In mathematical framework, the noncommutative probability is another name of quantum probability, and a quantum probability space consists of an -algebra of operators on a Hilbert space and a state (normalized positive linear functional) on the operator algebra. We study the basic notions in quantum probability theory comparing with the basic notions in classical (commutative) probability theory, and we also study the fundamental theory of quantum stochastic calculus motivated by the classical stochastic calculus.
Finally, we discuss several applications with future prospects of classical and quantum probability theory.
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List of Articles
카테고리 제목 소속 강연자
수학강연회 Congruences between modular forms file 서울대 유화종
수학강연회 Conformal field theory in mathematics file 고등과학원 강남규
수학강연회 Conformal field theory and noncommutative geometry file 동경대학교 Kawahigashi
수학강연회 Compressible viscous Navier-Stokes flows: Corner singularity, regularity file POSTECH 권재룡
수학강연회 Combinatorial Laplacians on Acyclic Complexes file 서울대학교 국웅
수학강연회 Codimension Three Conjecture file 교토대학교/서울대학교 Masaki Kashiwara
수학강연회 Cloaking via Change of Variables file KAIST 임미경
수학강연회 Classical and Quantum Probability Theory file 충북대학교 지운식
수학강연회 Class field theory for 3-dimensional foliated dynamical systems file Kyushu University Morishita Masanori
수학강연회 Circular maximal functions on the Heisenberg group file 연세대 수학과 김준일
수학강연회 Chern-Simons invariant and eta invariant for Schottky hyperbolic manifolds file KIAS 박진성
수학강연회 Categorification of Donaldson-Thomas invariants file 서울대학교 김영훈
수학강연회 Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras file Kyoto University/서울대학교 Masaki Kashiwara
수학강연회 Brownian motion with darning and conformal mappings file University of Washington Zhen-Qing Chen
수학강연회 Brownian motion and energy minimizing measure in negative curvature file 서울대학교 임선희
수학강연회 Birational Geometry of varieties with effective anti-canonical divisors file 연세대학교 최성락
수학강연회 Averaging formula for Nielsen numbers file 서강대학교 이종범
수학강연회 Arithmetic of elliptic curves file 서울대 김도형
수학강연회 Anomalous diffusions and fractional order differential equations file University of Washington Zhen-Qing Chen
수학강연회 Analytic torsion and mirror symmetry file Kyoto University Ken-ichi Yoshikawa
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