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이 항목의 수학노트 원문주소==
Pythagoras0 (토론 | 기여) 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
Pythagoras0 (토론 | 기여) 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
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| 1번째 줄: | 1번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">이 항목의 수학노트 원문주소 | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">이 항목의 수학노트 원문주소== |
| 5번째 줄: | 5번째 줄: | ||
| − | ==개요 | + | ==개요== |
* correspondence principle | * correspondence principle | ||
| 15번째 줄: | 15번째 줄: | ||
| − | ==1 | + | ==1== |
<math>*_{mn}</math> 은 transition <math>E_{m}\to E_{n}</math> 과 관계된 양들 | <math>*_{mn}</math> 은 transition <math>E_{m}\to E_{n}</math> 과 관계된 양들 | ||
| 36번째 줄: | 36번째 줄: | ||
| − | ==2 | + | ==2== |
* <math>[Q,P] = Q P - P Q = i \hbar</math> | * <math>[Q,P] = Q P - P Q = i \hbar</math> | ||
| 45번째 줄: | 45번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 2em;">3 | + | <h5 style="margin: 0px; line-height: 2em;">3== |
* <math>H(P,Q)</math> 해밀토니안<br> | * <math>H(P,Q)</math> 해밀토니안<br> | ||
| 53번째 줄: | 53번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 2em;">4 | + | <h5 style="margin: 0px; line-height: 2em;">4== |
* 운동방정식<br> | * 운동방정식<br> | ||
| 73번째 줄: | 73번째 줄: | ||
| − | ==역사 | + | ==역사== |
* 1925 Heisenberg matrix mechanics | * 1925 Heisenberg matrix mechanics | ||
| 86번째 줄: | 86번째 줄: | ||
| − | ==메모 | + | ==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). | 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). | ||
| 100번째 줄: | 100번째 줄: | ||
| − | ==관련된 항목들 | + | ==관련된 항목들== |
* [[푸리에 급수]] | * [[푸리에 급수]] | ||
| 108번째 줄: | 108번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">수학용어번역 | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">수학용어번역== |
* 단어사전<br> | * 단어사전<br> | ||
| 124번째 줄: | 124번째 줄: | ||
| − | ==매스매티카 파일 및 계산 리소스 | + | ==매스매티카 파일 및 계산 리소스== |
* | * | ||
| 139번째 줄: | 139번째 줄: | ||
| − | ==사전 형태의 자료 | + | ==사전 형태의 자료== |
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
| 151번째 줄: | 151번째 줄: | ||
| − | ==리뷰논문, 에세이, 강의노트 | + | ==리뷰논문, 에세이, 강의노트== |
* B. L. van der Waerden, [http://www.ams.org/notices/199703/vanderwaerden.pdf From Matrix Mechanics and Wave Mechanics to Unified Quantum Mechanics] | * B. L. van der Waerden, [http://www.ams.org/notices/199703/vanderwaerden.pdf From Matrix Mechanics and Wave Mechanics to Unified Quantum Mechanics] | ||
| 158번째 줄: | 158번째 줄: | ||
| − | ==관련논문 | + | ==관련논문== |
* http://www.jstor.org/action/doBasicSearch?Query= | * http://www.jstor.org/action/doBasicSearch?Query= | ||
| 168번째 줄: | 168번째 줄: | ||
| − | ==관련도서 | + | ==관련도서== |
* 도서내검색<br> | * 도서내검색<br> | ||
** http://books.google.com/books?q= | ** http://books.google.com/books?q= | ||
** http://book.daum.net/search/contentSearch.do?query= | ** http://book.daum.net/search/contentSearch.do?query= | ||
2012년 11월 1일 (목) 13:18 판
이 항목의 수학노트 원문주소==
개요
- correspondence principle
1
\(*_{mn}\) 은 transition \(E_{m}\to E_{n}\) 과 관계된 양들
\(Q=\left(q_{mn}e^{2\pi it\nu_{mn}}\right)\)
\(P=\left(p_{mn}e^{2\pi it\nu_{mn}}\right)\)
- 여기서 \(q_{mn},p_{mn}\) : amplitudes, \(\nu_{mn}\) : frequency 로 다음 조건을 만족시킴
- \(q_{mn}=q_{nm}^{*}\)
- \(p_{mn}=q_{nm}^{*}\)
- \(\nu_{mn}=-\nu_{nm}\)
- \(m \neq n\) 이면, \(\nu_{mn}\neq 0\)
- \(\nu_{rs}+\nu_{st}=\nu_{rt}\)
2
- \([Q,P] = Q P - P Q = i \hbar\)
- Born-Jordan condition 이라고도 불리며 보어-좀머펠트 양자 조건에 해당
3==
- \(H(P,Q)\) 해밀토니안
4==
- 운동방정식
- \(\dot{Q}_i=\partial H/\partial P\)
- \(\dot{P}=-\partial H/\partial Q\)
\(H(P,Q)\) 는 대각행렬이며, 고유값은 \(E_n\)
\(E_{m}-E_{n}=\hbar \nu_{mn}\)
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
관련도서
- \(q_{mn}=q_{nm}^{*}\)
- \(p_{mn}=q_{nm}^{*}\)
- \(\nu_{mn}=-\nu_{nm}\)
- \(m \neq n\) 이면, \(\nu_{mn}\neq 0\)
- \(\nu_{rs}+\nu_{st}=\nu_{rt}\)
- \(H(P,Q)\) 해밀토니안
4==
- 운동방정식
- \(\dot{Q}_i=\partial H/\partial P\)
- \(\dot{P}=-\partial H/\partial Q\)
\(H(P,Q)\) 는 대각행렬이며, 고유값은 \(E_n\)
\(E_{m}-E_{n}=\hbar \nu_{mn}\)
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