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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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  1. Randomness of prime numbers

  2. Space.Time.Noise

  3. 학부생을 위한 강연회: Tipping Point Analysis and Influence Maximization in Social Networks

  4. Role of Computational Mathematics and Image Processing in Magnetic Resonance Electrical Impedance Tomography (MREIT)

  5. On Ingram’s Conjecture

  6. Variational Methods without Nondegeneracy

  7. Chern-Simons invariant and eta invariant for Schottky hyperbolic manifolds

  8. Brownian motion with darning and conformal mappings

  9. Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras

  10. 학부생을 위한 강연회: 통신의 New Trend, 그리고 Big Data

  11. Cloaking via Change of Variables

  12. How to solve linear systems in practice

  13. Spectral Analysis for the Anomalous Localized Resonance by Plasmonic Structures

  14. Conformal field theory and noncommutative geometry

  15. 극소곡면의 등주부등식

  16. Topology of configuration spaces on graphs

  17. 학부생을 위한 강연회: What is the algebraic number theory?

  18. 정년퇴임 기념강연회: 숙제

  19. Integer partitions, q-series, and Modular forms

  20. Root multiplicities of hyperbolic Kac-Moody algebras and Fourier coefficients of modular forms

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