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수학:디락_델타_함수 [2016/05/24 16:13] – admin | 수학:디락_델타_함수 [2023/09/05 15:46] (current) – external edit 127.0.0.1 | ||
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- | ======적분 표현식====== | + | ======적분 표현====== |
$f(x)$의 [[: | $f(x)$의 [[: | ||
$$f(x) = \int_{-\infty}^\infty g(k) e^{ikx} dx$$ | $$f(x) = \int_{-\infty}^\infty g(k) e^{ikx} dx$$ | ||
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\begin{eqnarray} | \begin{eqnarray} | ||
\frac{1}{2\pi} \int_{-\infty}^\infty e^{ikx} dk &=& \lim_{\epsilon\rightarrow 0} \left[ \frac{1}{2\pi} \int_0^\infty e^{ikx-\epsilon x} dk + \frac{1}{2\pi} \int_{-\infty}^0 e^{ikx+\epsilon x} dk \right]\\ | \frac{1}{2\pi} \int_{-\infty}^\infty e^{ikx} dk &=& \lim_{\epsilon\rightarrow 0} \left[ \frac{1}{2\pi} \int_0^\infty e^{ikx-\epsilon x} dk + \frac{1}{2\pi} \int_{-\infty}^0 e^{ikx+\epsilon x} dk \right]\\ | ||
- | &=& \lim_{\epsilon\rightarrow 0} \left[ \frac{1}{\epsilon+ix} + \frac{1}{\epsilon-ix} \right]\\ | + | &=& \lim_{\epsilon\rightarrow 0} \frac{1}{2\pi} \left[ \frac{1}{\epsilon+ix} + \frac{1}{\epsilon-ix} \right]\\ |
&=& \lim_{\epsilon\rightarrow 0} \frac{\epsilon}{\pi(\epsilon^2 + x^2)} | &=& \lim_{\epsilon\rightarrow 0} \frac{\epsilon}{\pi(\epsilon^2 + x^2)} | ||
\end{eqnarray} | \end{eqnarray} | ||
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이라고 놓는다. | 이라고 놓는다. | ||
+ | ======함께 보기====== | ||
+ | [[: | ||