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Extra Form
Lecturer 지운식
Dept. 충북대학교
date Apr 14, 2011
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
Category Subject Dept. Lecturer
Math Colloquia Congruences between modular forms file 서울대 유화종
Math Colloquia Conformal field theory in mathematics file 고등과학원 강남규
Math Colloquia Conformal field theory and noncommutative geometry file 동경대학교 Kawahigashi
Math Colloquia Compressible viscous Navier-Stokes flows: Corner singularity, regularity file POSTECH 권재룡
Math Colloquia Combinatorial Laplacians on Acyclic Complexes file 서울대학교 국웅
Math Colloquia Codimension Three Conjecture file 교토대학교/서울대학교 Masaki Kashiwara
Math Colloquia Cloaking via Change of Variables file KAIST 임미경
Math Colloquia Classical and Quantum Probability Theory file 충북대학교 지운식
Math Colloquia Class field theory for 3-dimensional foliated dynamical systems file Kyushu University Morishita Masanori
Math Colloquia Circular maximal functions on the Heisenberg group file 연세대 수학과 김준일
Math Colloquia Chern-Simons invariant and eta invariant for Schottky hyperbolic manifolds file KIAS 박진성
Math Colloquia Categorification of Donaldson-Thomas invariants file 서울대학교 김영훈
Math Colloquia Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras file Kyoto University/서울대학교 Masaki Kashiwara
Math Colloquia Brownian motion with darning and conformal mappings file University of Washington Zhen-Qing Chen
Math Colloquia Brownian motion and energy minimizing measure in negative curvature file 서울대학교 임선희
Math Colloquia Birational Geometry of varieties with effective anti-canonical divisors file 연세대학교 최성락
Math Colloquia Averaging formula for Nielsen numbers file 서강대학교 이종범
Math Colloquia Arithmetic of elliptic curves file 서울대 김도형
Math Colloquia Anomalous diffusions and fractional order differential equations file University of Washington Zhen-Qing Chen
Math Colloquia Analytic torsion and mirror symmetry file Kyoto University Ken-ichi Yoshikawa
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