Video

# Classical and Quantum Probability Theory

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.
 Subject+ContentSubjectContentCommentUser NameNick NameUser IDTag
1. ### 학부학생을 위한 강연회: 기하학과 우주론

우리의 직관에 의하면 우주는 4차원으로 이루어져있다. 달리 말하면 우리가 어떤 사건을 기술 할 때 네 개의 숫자(공간3 + 시간1) 이면 충분하다는 것 이다. 세상에 다른 여분의 차원이 더 있다고 가정 여러 물리 법칙을 통일적으로 기술할 수 있음이 알려졌다...
CategoryMath Colloquia Dept.홍익대학교 Lecturer이남훈
2. ### <학부생을 위한 ɛ 강연> Mathematics and music: Pythagoras, Bach, Fibonacci and AI

In this talk, I will introduce the audience to the original beauty that leads to exploring the mathematical elements in music. I will cover the following topics on the connection between music and mathematics. - Harmonics & equations - ...
CategoryMath Colloquia Dept.피아니스트 Lecturer임현정
3. ### An equivalent condition to Bohr's for Dirichlet series

초록: SNU-abstract.pdf
CategoryMath Colloquia Dept.포항공대 Lecturer최윤성
4. ### A wrapped Fukaya category of knot complement and hyperbolic knot

상산수리과학관 20주년 기념강연
CategorySpecial Colloquia Dept.포항공대 Lecturer오용근
5. ### Noise-induced phenomena in stochastic heat equations

Stochastic heat equations (SHE) usually refer to heat equations perturbed by noise and can be a model for the density of diffusing particles under a random potential. When the irregularity of noise is dominating the diffusion, SHE exhibits ...
CategoryMath Colloquia Dept.포항공대 Lecturer김건우
6. ### Seoul ICM 2014 유치과정 개요 및 준비전략

국제수학자대회(ICM, International Congress of Mathematicians)는 1897년 쮜리히에서 처음 개최되었고, 매 4년마다 개최된다. 100여국 4천여 명 정도의 규모로 9일 동안 계속된다. 우리시대 최고의 수학자들이 참여하며, 필즈상(Fields Medal)을 개막식에서 ...
CategoryMath Colloquia Dept.포항공과대학교 Lecturer박형주
7. ### Iwasawa main conjecture and p-adic L-functions

The theory of L-functions and zeta functions have been the key subject of mathematical research during the centuries since the Riemann zeta function was introduced and its important connection to the arithmetic of the integer was recognized....
CategoryMath Colloquia Dept.포항공과대학교 Lecturer박지훈
8. ### 4-manifold topology and disk embedding

The disk embedding problem is of fundamental importance in the study of 4-dimensional topology. I will discuss its significance and difficulty, including how disk embedding makes dimension four intrinsically different from other dimensions. ...
CategoryMath Colloquia Dept.포항공과대학교 Lecturer차재춘
9. ### Restriction theorems for real and complex curves

We will talk about the Fourier restriction theorems for non-degenerate and degenerate curves in Euclidean space Rd. This problem was first studied by E. M. Stein and C. Fefferman for the circle and sphere, and it still remains an unsolved pr...
CategoryMath Colloquia Dept.포항공과대학교 Lecturer박종국
10. ### Trends to equilibrium in collisional rarefied gas theory

Dynamics of many particle system can be described by PDE of probability density function. The Boltzmann equation in kinetic theory is one of the most famous equation which describes rarefied gas dynamics. One of main property of the Boltzman...
CategoryMath Colloquia Dept.포항공과대학교 Lecturer이동현
11. ### Study stochastic biochemical systems via their underlying network structures

When a biological system is modeled using a mathematical process, the following step is normally to estimate the system parameters. Despite the numerous computational and statistical techniques, estimating parameters for complex systems can...
CategoryMath Colloquia Dept.포항공과대학교 Lecturer김진수
12. ### Vlasov-Maxwell equations and the Dynamics of Plasmas

In this colloquium talk, we study the Vlasov-Maxwell equations, a collisionless model in the field of kinetic theory. The model is a fundamental model for the dynamics of plasmas and was introduced in 1938 by Vlasov. Due to the hyperbolic n...
CategoryMath Colloquia Dept.포항공과대학교 Lecturer장진우
13. ### Infinite order rationally slice knots

A knot is a smooth embedding of an oriented circle into the three-sphere, and two knots are concordant if they cobound a smoothly embedded annulus in the three-sphere times the interval. Concordance gives an equivalence relation, and the se...
CategoryMath Colloquia Dept.카이스트 수리과학과 Lecturer박정환
14. ### Fermat´s last theorem

Fermat´s last theorem
CategoryMath Colloquia Dept.카이스트 Lecturer최서현
15. ### 1 is big enough to understand 3

We discuss how the closed connected 1-dimensional manifold, namely the circle, can help understanding 3-manifolds. We describe so-called the universal circle proposed by a lengendary mathematician, William Thurston, and discuss certain gene...
CategoryMath Colloquia Dept.카이스트 Lecturer백형렬
16. ### One and Two dimensional Coulomb Systems

Coulomb Gases are point processes consisting of particles whose pair interaction is governed by the Coulomb potential. There is also an external potential which confines the particles to a region. Wigner introduced this toy model for the Gi...
CategoryMath Colloquia Dept.카이스트 Lecturer폴정
17. ### <학부생을 위한 ɛ 강연> 복잡한 생명현상을 위한 21세기 현미경, 수학!

지난 50년간 진행된 분자생물학의 혁명으로 인해 생명 시스템이 수많은 분자들의 상호작용으로 구성되어 있음을 알게 되었습니다. 이러한 복잡한 시스템을 이해하기 위해서는 현미경과 같이 생명현상을 관찰하는 도구와 함께 수학은 생명과학 분야에서 필수적...
CategoryMath Colloquia Dept.카이스트 Lecturer김재경
18. ### Classical and Quantum Probability Theory

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 quantit...
CategoryMath Colloquia Dept.충북대학교 Lecturer지운식