"Spin system and Pauli exclusion principle"의 두 판 사이의 차이

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10번째 줄: 10번째 줄:
  
 
<h5>classical angular momentum</h5>
 
<h5>classical angular momentum</h5>
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<h5>고전역학의 각운동량</h5>
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* <math>\mathbf{L}=\mathbf{r}\times \mathbf{p}</math>
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*  A classical electron moving around a nucleus in a circular orbit<br>
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** orbital angular momentum, <math>L=m_evr</math>
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** magnetic dipole moment, <math>\mu= -evr/2</math>
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** where e, m_e, v, and r are the electron´s charge, mass, velocity, and radius, respectively.
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*  A classical electron of homogeneous mass and charge density rotating about a symmetry axis<br>
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** angular momentum, <math>L=(3/5)m_eR^2\Omega</math>
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** magnetic dipole moment, <math>\mu= -(3/10)eR^2\Omega</math>, where R and \Omega are the electron´s classical radius and rotating frequency
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*  gyromagnetic ratio <math>\gamma = \mu/L=-e/2m_e</math><br>[/pages/7141159/attachments/4562863 I15-62-g20.jpg]<br>
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* pictures from [http://universe-review.ca/R15-12-QFT.htm#g2 Gyromagnetic Ratio and Anomalous Magnetic Moment]
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<h5>operator formulation</h5>
 
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*  파울리 행렬 ([http://pythagoras0.springnote.com/pages/3063330 해밀턴의 사원수] 참조)<br><math>\sigma_1 = \sigma_x = \begin{pmatrix} 0&1\\ 1&0 \end{pmatrix} </math><br><math>\sigma_2 = \sigma_y = \begin{pmatrix} 0&-i\\ i&0 \end{pmatrix}  </math><br><math>\sigma_3 = \sigma_z = \begin{pmatrix} 1&0\\ 0&-1 \end{pmatrix}</math><br>
 
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*  raising and lowering 연산자<br><math>\sigma_{\pm}=\frac{1}{2}(\sigma_{x}\pm i\sigma_{y})</math><br><math>\sigma_{+}=\frac{1}{2}(\sigma_{x}+ i\sigma_{y})=\begin{pmatrix} 0&1\\ 0&0 \end{pmatrix}</math><br><math>\sigma_{-}=\frac{1}{2}(\sigma_{x}- i\sigma_{y})=\begin{pmatrix} 0&0\\ 1&0 \end{pmatrix}</math><br><math>[\sigma_{z},\sigma_{\pm}]=\pm 2\sigma_{\pm}</math><br>
 
  
 
 
 
 
63번째 줄: 88번째 줄:
  
 
* [[Dirac equation]]<br>
 
* [[Dirac equation]]<br>
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<h5>history</h5>
 
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* 1924 Pauli
 
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* 1925 Uhlenbeck and Goudsmit
 
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
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<h5>related items</h5>
 
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<h5>books</h5>
 
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* MICHELA MASSIMI  Pauli's Exclusion Principle: The Origin and Validation of a Scientific Principle 10.1093/bjps/axn056 [http://bjps.oxfordjournals.org/content/60/1/235.extract ]http://bjps.oxfordjournals.org/content/60/1/235.extract
 
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* The evolution of Pauli’s exclusion principle<br> Gordon N. Fleming http://www.personal.psu.edu/gnf1/blogs/flemin/Pauli%20Exclusion%20Prin.2007a.pdf
 
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* [[2010년 books and articles]]<br>
 
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 

2012년 6월 5일 (화) 05:24 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

 

고전역학의 각운동량

 

  • \(\mathbf{L}=\mathbf{r}\times \mathbf{p}\)

 

  • A classical electron moving around a nucleus in a circular orbit
    • orbital angular momentum, \(L=m_evr\)
    • magnetic dipole moment, \(\mu= -evr/2\)
    • where e, m_e, v, and r are the electron´s charge, mass, velocity, and radius, respectively.
  • A classical electron of homogeneous mass and charge density rotating about a symmetry axis
    • angular momentum, \(L=(3/5)m_eR^2\Omega\)
    • magnetic dipole moment, \(\mu= -(3/10)eR^2\Omega\), where R and \Omega are the electron´s classical radius and rotating frequency
  • gyromagnetic ratio \(\gamma = \mu/L=-e/2m_e\)
    [/pages/7141159/attachments/4562863 I15-62-g20.jpg]
  • pictures from Gyromagnetic Ratio and Anomalous Magnetic Moment

 

 

 

 

 

 

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.
  • 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.

 

 

 

 

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

 

 

Dirac wave equation[[search?q=dirac&parent id=6452627|]]
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