δ function - delta function

Japanese: δ関数 - デルタかんすう(英語表記)δ-function
δ function - delta function
A function introduced by P.A. Dirac to formulate quantum mechanics. Even though δ( x )=0 when x ≠0, the integral in any domain including the point x =0 is
A function δ( x ) is a function that satisfies the following: For any function f ( x ) that is continuous at x = 0,
may be defined as a function that satisfies. However, the integration domain can be any as long as it includes x = 0. δ( x ) has a strong singularity at x = 0, so it cannot be considered an ordinary function, but mathematically it has a rigorous basis as a generalized function. δ( x ) can also be expressed as the limit of the function sin gxx as g → ∞. By the definition of δ( x ), δ( -x ) = δ( x ), so δ( x ) is an even function, and δ'(- x ) = -δ'( x ), so δ'( x ) is an odd function.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:
量子力学を定式化するために,P.A.M.ディラックが導入した関数。 x≠0 のとき δ(x)=0 であるにもかかわらず,x=0 の点を含む任意の領域での積分が
を満足するような関数 δ(x) のことをいう。あるいは,x=0 で連続な任意の関数 f(x) に対して,
を満足する関数と定義してもよい。ただし,積分領域は x=0 を含んでいれば任意でよい。 δ(x) は x=0 で強い特異性をもつから,通常の関数とはいえないが,数学的には超関数として厳密な基礎づけがなされている。 δ(x) は, sin gxx という関数の g→∞ の極限として表わすこともできる。 δ(x) の定義によって,δ(-x)=δ(x) となるから δ(x) は偶関数,また δ'(-x)=-δ'(x) となるから δ'(x) は奇関数である。

出典 ブリタニカ国際大百科事典 小項目事典ブリタニカ国際大百科事典 小項目事典について 情報

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