"Spin system and Pauli exclusion principle"의 두 판 사이의 차이
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2012년 6월 5일 (화) 06:19 판
introduction
- the simplest example of quantum mechanical system
- quantization of the angular momentum
- measures as being some multiple of Planck's constant divided by 2pi
classical angular momentum
representation theory
- concept from the representation of \(SU(2)\)
- half of highest weight is called the spin of the module
- Casimir operator can also detect this number.
- Casimir operator can also detect this number.
- spin \(1/2\) is the most important case since they are the matter particles
- this is why we have half-integral spin although those representation are integral highest weight representations.
operator formulation
- 파울리 행렬 (해밀턴의 사원수 참조)
\(\sigma_1 = \sigma_x = \begin{pmatrix} 0&1\\ 1&0 \end{pmatrix} \)
\(\sigma_2 = \sigma_y = \begin{pmatrix} 0&-i\\ i&0 \end{pmatrix} \)
\(\sigma_3 = \sigma_z = \begin{pmatrix} 1&0\\ 0&-1 \end{pmatrix}\) - raising and lowering 연산자
\(\sigma_{\pm}=\frac{1}{2}(\sigma_{x}\pm i\sigma_{y})\)
\(\sigma_{+}=\frac{1}{2}(\sigma_{x}+ i\sigma_{y})=\begin{pmatrix} 0&1\\ 0&0 \end{pmatrix}\)
\(\sigma_{-}=\frac{1}{2}(\sigma_{x}- i\sigma_{y})=\begin{pmatrix} 0&0\\ 1&0 \end{pmatrix}\)
\([\sigma_{z},\sigma_{\pm}]=\pm 2\sigma_{\pm}\)
sl(2)
- commutator
\([E,F]=H\)
\([H,E]=2E\)
\([H,F]=-2F\)
spin particle statstics
- Bosons
- photon
- vector boson
- Gluon
- follows Bose-Einstein statistics
- force-transmitting particles
- Fermions = spin- \(1/2\) particles
- quarks and leptons
- follows Fermi-Dirac statistics
- matter particles
- quarks and leptons
Dirac wave equation[[search?q=dirac&parent id=6452627|]]
history
- 1924 Pauli
- 1925 Uhlenbeck and Goudsmit
- http://www.google.com/search?hl=en&tbs=tl:1&q=
books
- MICHELA MASSIMI Pauli's Exclusion Principle: The Origin and Validation of a Scientific Principle 10.1093/bjps/axn056 [1]http://bjps.oxfordjournals.org/content/60/1/235.extract
- The evolution of Pauli’s exclusion principle
Gordon N. Fleming http://www.personal.psu.edu/gnf1/blogs/flemin/Pauli%20Exclusion%20Prin.2007a.pdf - 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=