"행렬 역학"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
 
(사용자 2명의 중간 판 23개는 보이지 않습니다)
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>
+
==개요==
  
−
 
+
* correspondence principle
  
−
 
+
* http://www.eolss.net/Sample-Chapters/C05/E6-06B-09-00.pdf
  
−
<h5>개요</h5>
+
  
−
 
+
  
−
보어 모형
+
==1==
  
−
correspondence principle
+
<math>*_{mn}</math> 은 transition <math>E_{m}\to E_{n}</math> 과 관계된 양들
  
−
 
+
  
−
 
+
<math>Q=\left(q_{mn}e^{2\pi it\nu_{mn}}\right)</math>
  
−
* <math>[X,P] = X P - P X = i \hbar</math>
+
<math>P=\left(p_{mn}e^{2\pi it\nu_{mn}}\right)</math>
  
−
 
+
*  여기서 <math>q_{mn},p_{mn}</math> : amplitudes, <math>\nu_{mn}</math> : frequency 로 다음 조건을 만족시킴
 +
** <math>q_{mn}=q_{nm}^{*}</math>
 +
** <math>p_{mn}=q_{nm}^{*}</math>
 +
** <math>\nu_{mn}=-\nu_{nm}</math>
 +
** <math>m \neq n</math> 이면, <math>\nu_{mn}\neq 0</math>
 +
** <math>\nu_{rs}+\nu_{st}=\nu_{rt}</math>
  
−
<h5>역사</h5>
+
 +
 
 +
 +
 
 +
==2==
 +
 
 +
* <math>[Q,P] = Q P - P Q = i \hbar</math>
 +
* Born-Jordan condition 이라고도 불리며 보어-좀머펠트 양자 조건에 해당
 +
 
 +
 +
 
 +
 +
 
 +
==3==
 +
 
 +
* <math>H(P,Q)</math>  해밀토니안
 +
 
 +
 +
 
 +
 +
 
 +
==4==
 +
 
 +
*  운동방정식
 +
* <math>\dot{Q}_i=\partial H/\partial P</math>
 +
* <math>\dot{P}=-\partial H/\partial Q</math>
 +
 
 +
 +
 
 +
 +
 
 +
<math>H(P,Q)</math> 는 대각행렬이며, 고유값은 <math>E_n</math>
 +
 
 +
<math>E_{m}-E_{n}=\hbar \nu_{mn}</math>
 +
 
 +
 +
 
 +
 +
 
 +
 +
 
 +
==역사==
  
 
* 1925 Heisenberg matrix mechanics
 
* 1925 Heisenberg matrix mechanics
28번째 줄: 74번째 줄:
 
* 1930-31 Stone-von Neuman Theorem
 
* 1930-31 Stone-von Neuman Theorem
 
* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
* http://www.google.com/search?hl=en&tbs=tl:1&q=
−
* [[수학사연표 (역사)|수학사연표]]
+
* [[수학사 연표]]
  
−
 
+
  
−
 
+
  
−
<h5>메모</h5>
+
==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).
  
−
* [http://www.worldscibooks.com/etextbook/7271/7271_chap02.pdf ]http://www.worldscibooks.com/etextbook/7271/7271_chap02.pdf
+
* http://www.worldscibooks.com/etextbook/7271/7271_chap02.pdf
−
* A brief history of the mathematical equivalence between the two
+
* [http://dialnet.unirioja.es/servlet/fichero_articulo?codigo=2735593 A brief history of the mathematical equivalence between the two quantum mechanics]
 +
* [http://philsci-archive.pitt.edu/3658/ Why were two theories (Matrix Mechanics and Wave Mechanics) deemed logically distinct, and yet equivalent, in Quantum Mechanics?]
 
* Quantum Mechanics: Concepts and Applications
 
* Quantum Mechanics: Concepts and Applications
 
* Math Overflow http://mathoverflow.net/search?q=
 
* Math Overflow http://mathoverflow.net/search?q=
  
−
 
+
  
−
 
+
  
−
<h5>관련된 항목들</h5>
+
==관련된 항목들==
  
−
 
+
* [[푸리에 급수]]
  
−
 
+
  
−
<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>
+
  
−
*  단어사전<br>
+
==수학용어번역==
 +
 
 +
*  단어사전
 
** http://translate.google.com/#en|ko|
 
** http://translate.google.com/#en|ko|
 
** http://ko.wiktionary.org/wiki/
 
** http://ko.wiktionary.org/wiki/
−
* 발음사전 http://www.forvo.com/search/
+
* 발음사전 http://www.forvo.com/search/
−
* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
+
* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]
 
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
 
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
 
* [http://www.kss.or.kr/pds/sec/dic.aspx 한국통계학회 통계학 용어 온라인 대조표]
 
* [http://www.kss.or.kr/pds/sec/dic.aspx 한국통계학회 통계학 용어 온라인 대조표]
 
* [http://www.nktech.net/science/term/term_l.jsp?l_mode=cate&s_code_cd=MA 남·북한수학용어비교]
 
* [http://www.nktech.net/science/term/term_l.jsp?l_mode=cate&s_code_cd=MA 남·북한수학용어비교]
−
* [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
+
* [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
  
−
 
+
  
−
 
+
  
−
<h5>매스매티카 파일 및 계산 리소스</h5>
+
==매스매티카 파일 및 계산 리소스==
  
−
*  
+
*
 
* http://www.wolframalpha.com/input/?i=
 
* http://www.wolframalpha.com/input/?i=
 
* http://functions.wolfram.com/
 
* http://functions.wolfram.com/
80번째 줄: 129번째 줄:
 
* [https://docs.google.com/open?id=0B8XXo8Tve1cxMWI0NzNjYWUtNmIwZi00YzhkLTkzNzQtMDMwYmVmYmIxNmIw 매스매티카 파일 목록]
 
* [https://docs.google.com/open?id=0B8XXo8Tve1cxMWI0NzNjYWUtNmIwZi00YzhkLTkzNzQtMDMwYmVmYmIxNmIw 매스매티카 파일 목록]
  
−
 
+
  
−
 
+
  
−
<h5>사전 형태의 자료</h5>
+
==사전 형태의 자료==
  
 
* http://ko.wikipedia.org/wiki/
 
* http://ko.wikipedia.org/wiki/
92번째 줄: 141번째 줄:
 
* [http://eqworld.ipmnet.ru/ The World of Mathematical Equations]
 
* [http://eqworld.ipmnet.ru/ The World of Mathematical Equations]
  
−
 
+
  
−
 
+
  
−
<h5>리뷰논문, 에세이, 강의노트</h5>
+
==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]
 +
* 임경순, [http://www.postech.ac.kr/press/pp/part02/ch110/sec040/ 행렬역학의 전개 과정]
  
−
 
+
−
 
 
−
 
 
−
 
 
−
<h5>관련논문</h5>
 
−
 
 
−
* http://www.jstor.org/action/doBasicSearch?Query=
 
−
* http://www.ams.org/mathscinet
 
−
* http://dx.doi.org/
 
  
−
 
 
  
−
 
 
  
−
<h5>관련도서</h5>
+
  
−
* 도서내검색<br>
+
   
−
** http://books.google.com/books?q=
+
[[분류:양자역학]]
−
** http://book.daum.net/search/contentSearch.do?query=
+
[[분류:수리물리학]]

2020년 12월 28일 (월) 04:12 기준 최신판

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



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).



관련된 항목들



수학용어번역



매스매티카 파일 및 계산 리소스



사전 형태의 자료



리뷰논문, 에세이, 강의노트

원본 주소 "https://wiki.mathnt.net/index.php?title=행렬_역학&oldid=48333"