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Statements

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dbr:Canonical_transformation
dbo:wikiPageWikiLink
dbr:Generating_function_(physics)
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Generating function (physics) 正則變換生成函數 모함수 (물리학)
rdfs:comment
在哈密頓力學裏，當計算正則變換時，生成函數扮演的角色，好似在兩組正則坐標 ， 之間的一座橋。為了要保證正則變換的正確性 ，採取一種間接的方法，稱為生成函數方法。這兩組變數必須符合方程式 ；(1) 其中， 是舊廣義坐標， 是舊廣義動量， 是新廣義坐標， 是新廣義動量， 分別為舊哈密頓量與新哈密頓量， 是生成函數， 是時間。 生成函數 的參數，除了時間以外，一半是舊的正則坐標；另一半是新的正則坐標。視選擇出來不同的變數而定，一共有四種基本的生成函數。每一種基本生成函數設定一種不同的變換，從舊的一組正則坐標變換為新的一組正則坐標。這變換 保證是正則變換。 ( 이 문서는 해밀턴 역학에서 좌표 변환에 쓰이는 함수에 관한 것입니다. 조합론에서 쓰이는 생성함수(generating function)에 대해서는 생성함수 (수학) 문서를 참고하십시오.) 해밀턴 역학에서 모함수(母函數, generating function)는 두 개의 일반화 좌표간의 정준변환을 연결해주는 함수이다. In physics, and more specifically in Hamiltonian mechanics, a generating function is, loosely, a function whose partial derivatives generate the differential equations that determine a system's dynamics. Common examples are the partition function of statistical mechanics, the Hamiltonian, and the function which acts as a bridge between two sets of canonical variables when performing a canonical transformation.
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dbo:abstract
In physics, and more specifically in Hamiltonian mechanics, a generating function is, loosely, a function whose partial derivatives generate the differential equations that determine a system's dynamics. Common examples are the partition function of statistical mechanics, the Hamiltonian, and the function which acts as a bridge between two sets of canonical variables when performing a canonical transformation. ( 이 문서는 해밀턴 역학에서 좌표 변환에 쓰이는 함수에 관한 것입니다. 조합론에서 쓰이는 생성함수(generating function)에 대해서는 생성함수 (수학) 문서를 참고하십시오.) 해밀턴 역학에서 모함수(母函數, generating function)는 두 개의 일반화 좌표간의 정준변환을 연결해주는 함수이다. 在哈密頓力學裏，當計算正則變換時，生成函數扮演的角色，好似在兩組正則坐標 ， 之間的一座橋。為了要保證正則變換的正確性 ，採取一種間接的方法，稱為生成函數方法。這兩組變數必須符合方程式 ；(1) 其中， 是舊廣義坐標， 是舊廣義動量， 是新廣義坐標， 是新廣義動量， 分別為舊哈密頓量與新哈密頓量， 是生成函數， 是時間。 生成函數 的參數，除了時間以外，一半是舊的正則坐標；另一半是新的正則坐標。視選擇出來不同的變數而定，一共有四種基本的生成函數。每一種基本生成函數設定一種不同的變換，從舊的一組正則坐標變換為新的一組正則坐標。這變換 保證是正則變換。
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