행렬 역학
http://bomber0.myid.net/ (토론)님의 2012년 6월 7일 (목) 03:42 판
이 항목의 수학노트 원문주소
개요
보어-좀머펠트 양자 조건
correspondence principle
1
\(Q=\left(q_{mn}e^{2\pi it\nu_{mn}}\right)\)
\(P=\left(p_{mn}e^{2\pi it\nu_{mn}}\right)\)
\(q_{mn},p_{mn}\) : amplitudes
\(\nu_{mn}\) : frequency
\(q_{mn}=q_{nm}^{*}\)
\(p_{mn}=q_{nm}^{*}\)
\(\nu_{mn}=-\nu_{nm}\)
\(m \neq n\) 이면, \(\nu_{mn}\neq 0\)
\(\nu_{rs}+\nu_{st}=\nu_{rt}\)
2
- Born-Jordan condition
- \([Q,P] = Q P - P Q = i \hbar\)
3
- \(H(P,Q)\) 는 대각행렬이며,
4
- 운동방정식
- \(\dot{Q}_i=\partial H/\partial P\)
- \(\dot{P}=-\partial H/\partial Q\)
역사
- 1925 Heisenberg matrix mechanics
- 1926 Pauli hydrogen atom
- 1927 Heisenberg uncertainty principle
- 1930-31 Stone-von Neuman Theorem
- http://www.google.com/search?hl=en&tbs=tl:1&q=
- 수학사연표
메모
On the other hand, matrix mechanics was invented by Heisenberg in June 1925, and presented in a fully developed form in Dirac’s first paper on quantum mechanics (received 7 November 1925) and also in the famous “three-men’s paper” of Born, Heisenberg and Jordan (received 16 November 1925).
- http://www.worldscibooks.com/etextbook/7271/7271_chap02.pdf
- A brief history of the mathematical equivalence between the two quantum mechanics
- Why were two theories (Matrix Mechanics and Wave Mechanics) deemed logically distinct, and yet equivalent, in Quantum Mechanics?
- Quantum Mechanics: Concepts and Applications
- Math Overflow http://mathoverflow.net/search?q=
관련된 항목들
수학용어번역
- 단어사전
- 발음사전 http://www.forvo.com/search/
- 대한수학회 수학 학술 용어집
- 한국통계학회 통계학 용어 온라인 대조표
- 남·북한수학용어비교
- 대한수학회 수학용어한글화 게시판
매스매티카 파일 및 계산 리소스
- 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://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
- B. L. van der Waerden, From Matrix Mechanics and Wave Mechanics to Unified Quantum Mechanics
- 임경순, 행렬역학의 전개 과정
관련논문