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| 배규호:교차영역 [2017/06/30 18:04] – bekuho | 배규호:교차영역 [2023/09/05 15:46] (current) – external edit 127.0.0.1 |
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| \begin{equation*} | \begin{equation*} |
| \begin{split} | \begin{split} |
| \Gamma_{fi} &\propto V\Big<\Big|\int d^{d}x\sigma_k e^{-i(p_f-p_i)x}\Big|^{2}\Big>_{\{\sigma_k\}}\\ | \Gamma_{fi} &\propto (1/V)\Big<\Big|\int d^{d}x\sum_{k} \sigma_k e^{ikx} e^{-i(p_f-p_i)x}\Big|^{2}\Big>_{\{\sigma_k\}}, \quad k = p_f - p_i \\ |
| &\propto V\Big<\Big|\sigma_k \int d^{d}x e^{-i(p_f-p_i)x}\Big|^{2}\Big>_{\{\sigma_k\}}\\ | &\propto V\Big<\Big|\sum_{k}\sigma_k\Big|^{2}\Big>_{\{\sigma_k\}} \\ |
| &\propto V\Big<\Big|\sigma_k\Big|^{2}\Big>_{\{\sigma_k\}}, \quad p_f - p_i = k =0 | &\propto V\sum_{k}\Big<\Big|\sigma_k\Big|^{2}\Big>_{\{\sigma_k\}} |
| \end{split} | \end{split} |
| \end{equation*} | \end{equation*} |