각운동량의 양자 이론

이 항목의 수학노트 원문주소

• 각운동량의 양자화

 

 

 

 

 

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 \(\gamma = \mu/L=-e/2m_e\)
  I15-62-g20.jpg
  
• pictures from Gyromagnetic Ratio and Anomalous Magnetic Moment

 

 

 

 

 

 

3j symbols

• relation between 3j-symbol and Clebsch-Gordan coefficient
• Racah formula for 3j-symbol
  
  • explicit formula
• orthogonality relation
• Wigner-Eckart theorem
• 테이블
  
  • http://www.eng.fsu.edu/~dommelen/quantum/style_a/clgrdn.html#sec:clgrdn
  • http://www.eng.fsu.edu/~dommelen/quantum/style_a/nt_cgct.html#sec:nt_cgct
• 강의
  
  • http://www.youtube.com/watch?v=KZe6LqSMW9Y&feature=relmfu

 

 

역사

 

• http://www.google.com/search?hl=en&tbs=tl:1&q=
• 수학사연표

 

 

메모

• Semiclassical analysis ofWigner 3j-symbol http://bohr.physics.berkeley.edu/hal/pubs/AqHaLiYu2007/AqHaLiYuJPA3jSymbol.pdf
• example
  
  • [1]http://www.nyu.edu/classes/tuckerman/quant.mech/lectures/lecture_8/node3.html
  • http://www.physicsforums.com/showthread.php?t=172397
• Math Overflow http://mathoverflow.net/search?q=

 

 

 

 

수학용어번역

• 단어사전
  
  • http://translate.google.com/#en%7Cko%7C
  • http://ko.wiktionary.org/wiki/
• 발음사전 http://www.forvo.com/search/
• 대한수학회 수학 학술 용어집
  
  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
• 한국통계학회 통계학 용어 온라인 대조표
• 남·북한수학용어비교
• 대한수학회 수학용어한글화 게시판

 

 

매스매티카 파일 및 계산 리소스

• http://demonstrations.wolfram.com/AdditionOfAngularMomentaInQuantumMechanics/
• http://www.wolframalpha.com/input/?i=
• http://functions.wolfram.com/
• NIST Digital Library of Mathematical Functions
• Abramowitz and Stegun Handbook of mathematical functions
• The On-Line Encyclopedia of Integer Sequences
• Numbers, constants and computation
• 매스매티카 파일 목록

 

 

사전 형태의 자료

• http://mathworld.wolfram.com/Clebsch-GordanCoefficient.html
• http://mathworld.wolfram.com/RacahV-Coefficient.html
• http://mathworld.wolfram.com/Wigner3j-Symbol.html
  
• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• The Online Encyclopaedia of Mathematics
• NIST Digital Library of Mathematical Functions
• The World of Mathematical Equations

 

 

리뷰논문, 에세이, 강의노트

• Paul E.S. Wormer, ANGULAR MOMENTUM THEORY
• Quantization of the Spins

 

 

관련논문

• http://www.jstor.org/action/doBasicSearch?Query=
• http://www.ams.org/mathscinet
• http://dx.doi.org/

 

 

관련도서

• 도서내검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/contentSearch.do?query=