{"id":8933,"date":"2010-02-17T15:34:00","date_gmt":"2010-02-17T15:34:00","guid":{"rendered":"http:\/\/melotopia.net\/b\/?p=8933"},"modified":"2010-02-17T15:34:00","modified_gmt":"2010-02-17T15:34:00","slug":"%ed%91%b8%eb%a6%ac%ec%97%90-%eb%b3%80%ed%99%98%ec%9d%98-basis","status":"publish","type":"post","link":"http:\/\/melotopia.net\/b\/?p=8933","title":{"rendered":"\ud478\ub9ac\uc5d0 \ubcc0\ud658\uc758 basis"},"content":{"rendered":"
\n \ud478\ub9ac\uc5d0 \ubcc0\ud658\uc744 \ud560\ub54c exp(ikx)\ub97c \uacf1\ud574\uc11c \uc801\ubd84\ud55c\ub2e4\ub294 \uac74 \uc694\uc0c8\ub294 \ub300\ud559\uc0dd\ub4e4\ub3c4 \uc544\ub294 \uc0ac\uc2e4\uc774\ub2e4.<\/p>\n

\uc65c?<\/p>\n


\n http:\/\/snowall.tistory.com\/182
\n <\/a><\/p>\n

\uc77c\ub2e8, \uc9c0\uc218\ud568\uc218\uac00 \ubbf8\ubd84\uacfc \uc801\ubd84\uc5d0 \ub300\ud574\uc11c \uace0\uc720\ud568\uc218\ub77c\ub294 \uac83\uc740 \uc54c\ub824\uc838 \uc788\ub2e4. \uc544\ubb34\ud2bc \ubbf8\ubd84\uacfc \uc801\ubd84\uc740 \ud568\uc218 \uacf5\uac04\uc5d0\uc11c\uc758 \uc120\ud615\ubcc0\ud658\uc778\ub370, \ubc14\ub85c \uadf8 \uc120\ud615\ubcc0\ud658\uc5d0 \ub300\ud55c \uace0\uc720\ud568\uc218\uc774\ub2e4.<\/p>\n

\ud568\uc218 \uacf5\uac04\uc744 \ubca1\ud130 \uacf5\uac04\uc774\ub77c\uace0 \ud560 \ub54c, \ub450 \ud568\uc218\ub97c \uacf1\ud574\uc11c \uc804\uccb4 \uc815\uc758\uc5ed\uc5d0 \ub300\ud574 \uc801\ubd84\ud558\ub294 \uac83\uc740 \ub450 \ud568\uc218\uc758 \ub0b4\uc801\uc744 \uad6c\ud558\ub294 \uac83\uc774\ub2e4. \ub9cc\uc57d \ub458\uc911 \ud558\ub098\uac00 basis\ubca1\ud130\ub77c\uba74, \uadf8 \ubca1\ud130\uc758 \ud2b9\uc815 \ubc29\ud5a5\uc5d0 \ub300\ud55c \uc88c\ud45c\uac12\uc744 \uc54c \uc218 \uc788\uac8c \ub41c\ub2e4. \uadf8\ub7fc, \uc9c0\uc218\ud568\uc218\uac00 \uc5b4\uc9f8\uc11c \uadf8\ub7f0 \ud568\uc218\uacf5\uac04\uc758 basis\ub97c \uad6c\uc131\ud558\ub294\uc9c0 \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n

basis\uac00 \ub418\uae30 \uc704\ud574\uc11c\ub294, \uc9d1\ud569\uc758 \uc6d0\uc18c\ub4e4\uc774 \uc11c\ub85c \uc120\ud615 \ub3c5\ub9bd\uc774\uc5b4\uc57c \ud558\uace0, \uc9d1\ud569\uc758 \uc6d0\uc18c\ub4e4\uc758 \uc120\ud615 \uacb0\ud569\uc73c\ub85c \ubaa8\ub4e0 \uc6d0\uc18c\ub97c \ub098\ud0c0\ub0bc \uc218 \uc788\uc5b4\uc57c \ud55c\ub2e4.<\/p>\n

1. \uc120\ud615 \ub3c5\ub9bd
\n
\n exp(ikx)\ub97c x\uc5d0 \ub300\ud55c \ud568\uc218\ub77c \ud558\uace0 k\ub97c \uc778\ub371\uc2a4\ub77c\uace0 \ubd80\ub974\uc790. \uadf8\ub7fc \uc778\ub371\uc2a4\uac00 \ub2e4\ub974\uba74 \ub2e4\ub978 \ud568\uc218\uac00 \ub41c\ub2e4. \uc774 \ud568\uc218\ub4e4\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \uc131\uc9c8\uc744 \ub9cc\uc871\ud55c\ub2e4.
\n
\n $\\int exp(ikx)exp(-ilx) dx = \\delta(k-l)$
\n
\n $\\delta(x)$\ub294 x=0\uc774\uba74 \uc815\uc758\ub418\uc9c0 \uc54a\uc9c0\ub9cc, x=0\uc774 \uc544\ub2cc \ubaa8\ub4e0 \uad6c\uac04\uc5d0\uc11c 0\uc73c\ub85c \uc815\uc758\ub418\uba70, $\\int \\delta(x) dx = 1$\uc744 \ub9cc\uc871\ud558\ub294 \ud568\uc218\uc774\ub2e4. \uc774\ub984\uc740 \ub514\ub799\uc758 \ub378\ud0c0 \ud568\uc218\uc774\ub2e4.
\n
\n
\n
\n [\uac01\uc8fc:
\n <\/span>
\n 1
\n
\n ]
\n <\/span>
\n<\/a>
\n<\/sup>
\n \ud06c\ub85c\ub124\ucee4 \ub378\ud0c0\uc758 \uc5f0\uc18d\ud568\uc218 \ubc84\uc804\uc778\ub370, \uc544\ubb34\ud2bc, \uc5b4\ub5a4 \ud2b9\uc815\ud55c k\uc5d0 \ub300\ud574\uc11c \uc120\ud615 \ub3c5\ub9bd\uc774 \uc544\ub2c8\ub77c\uace0 \ud558\uc790. \uadf8\ub7fc \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f8 \uc218 \uc788\uc5b4\uc57c \ud55c\ub2e4.
\n
\n $exp(ikx)=\\sum A(n)exp(inx) $
\n
\n \ub2e8, \uc704\uc758 \uae09\uc218\uc5d0\uc11c n=k\uc778 \uacbd\uc6b0\ub294 \ube7c\uc790.
\n
\n \uadf8\ub7fc, \ub2e4\uc74c\uacfc \uac19\uc740 \ub9c8\uc220\uc744 \ubd80\ub824\ubcfc \uc218 \uc788\uac8c \ub41c\ub2e4.
\n
\n $\\delta(k-k)=\\int exp(ikx)exp(-ikx) = \\int \\sum A(n) exp(inx) exp(-ikx) dx= \\sum A(n) \\int exp(inx)exp(-ikx)dx = \\sum A(n) \\delta(n-k)$
\n
\n \uadfc\ub370 \ub09c n=k\uc778 \uacbd\uc6b0\ub294 \ube7c\uc790\uace0 \ud588\ub2e4. \ub530\ub77c\uc11c, \uc774 \uacc4\uc0b0\uc758 \uc88c\ubcc0\uc740 0\uc774 \uc544\ub2c8\uace0 \uc6b0\ubcc0\uc740 0\uc774\ub2e4. \uc774\ub7f0 \ubb63\uac19\uc740 \uc77c\uc774 \uc77c\uc5b4\ub09c \uc774\uc720\ub294 \uc804\ubd80 \uc560\ucd08\uc5d0 \uc598\ub4e4\uc774 \uc120\ud615 \ub3c5\ub9bd\uc774 \uc544\ub2c8\ub77c\uace0 \uac00\uc815\ud588\uae30 \ub54c\ubb38\uc774\ub2e4. \ub530\ub77c\uc11c \uadf8 \uac00\uc815\uc744 \ubd80\uc815\ud558\uace0 \ud3b8\ud55c \ub9c8\uc74c\uc73c\ub85c \uc774\ub4e4\uc774 \uc120\ud615 \ub3c5\ub9bd\uc774\ub77c\ub294 \uac83\uc744 \ubc1b\uc544\ub4e4\uc774\uc790.<\/p>\n

\uc544, \uc77c\ub2e8 n\uc774 \uc5f0\uc18d\uc778 \uacbd\uc6b0\ub3c4 \ub2e4\ub904\uc57c\uaca0\ub2e4. \uadf8\ub7fc \uadf8\ub300\ub85c \ub2e4\uc74c\uacfc \uac19\uc774 \ubc14\uafb8\uba74 \ub41c\ub2e4.
\n
\n $\\delta(k-k)=\\int exp(ikx)exp(-ikx) dx = \\int \\int A(n) exp(inx) exp(-ikx)
\ndn dx= \\int A(n)dn \\int exp(inx)exp(-ikx)dx = \\int A(n) \\delta(n-k) dn$
\n
\n \ubb3c\ub860 \uc5ec\uae30\uc11c\ub3c4 \uc801\ubd84\ud560 \ub54c n=k\uc778 \ub531 \ud55c\uc810\ub9cc \ube7c\uace0 \ub2e4 \uc9c0\ub098\uac04\ub2e4.<\/p>\n

2. \ud45c\ud604 \uac00\ub2a5\uc131
\n
\n \uc5b4\ub5a4 \ud568\uc218 f(x)\uac00 \uc788\ub2e4\uace0 \ud558\uc790. \uadf8\ub7fc \uc774 \ud568\uc218\ub97c exp(ikx)\ub85c \ud45c\ud604\ud558\uace0 \uc2f6\uc73c\uba74 \uc77c\ub2e8 \ub2e4\uc74c\uacfc \uac19\uc774 \ud558\uc790.
\n
\n $f(x)=\\int \\hat{f}(k) exp(-ikx) dk$
\n
\n \ubb3c\ub860, \uc5ec\uae30\uc11c $\\hat{f}(k) = \\int f(x) exp(ikx) dx$ \uc774\ub2e4.
\n
\n \uc774\uac8c \uc65c \ub418\ub098 \uc0b4\ud3b4\ubcf4\uc790.
\n
\n $f(x) = \\int \\int f(y) exp(iky) dy exp(-ikx) dk = \\int\\int f(y) exp(ik(y-x))dy dk = \\int f(y)\\delta(y-x) dy $
\n
\n \uadfc\ub370, \ub514\ub799\uc758 \ub378\ud0c0 \ud568\uc218\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uc131\uc9c8\uc774 \uc788\ub2e4.
\n
\n $\\int \\delta(y-x) f(x) dx = f(y)$
\n
\n y\uc5d0 \ubb50\uac00 \uc788\ub4e0\uc9c0\uac04\uc5d0 f(x)\uc5d0\ub2e4\uac00 y\ub97c \ub300\uc785\ud574\uc8fc\ub294, \ubb50 \uadf8\ub7f0 \uc131\uc9c8\uc774\ub2e4. \ub530\ub77c\uc11c \uc704\uc758 \ub4f1\uc2dd\uc740 \uc131\ub9bd\ud55c\ub2e4. \uc801\ubd84 \uc21c\uc11c\ub97c \ubc14\uafd4\uc8fc\ub294\uac74 \uc5c4\ubc00\ud788 \uc124\uba85\ud558\uc9c0\ub294 \uc54a\uc558\uc9c0\ub9cc
\n
\n
\n
\n [\uac01\uc8fc:
\n <\/span>
\n 2
\n
\n ]
\n <\/span>
\n<\/a>
\n<\/sup>
\n \uc544\ubb34\ud2bc \uc218\ub834\ud558\uba74 \uadf8\ub798\ub3c4 \ub41c\ub2e4\ub294 \uac83\uc774 \uc54c\ub824\uc838 \uc788\ub2e4.<\/p>\n

\ub530\ub77c\uc11c exp(ikx)\ub294 \ud568\uc218 \uacf5\uac04\uc758 basis\ub85c \uc4f8 \uc218 \uc788\ub2e4.<\/p>\n

<\/p>\n

\n
    \n
  1. \n \uc5b4\ub290 \uc774\uc0c1\ud55c \ub098\ub77c\uc758 \ud2b9\uc218\ubd80\ub300\uc778 \ub378\ud0c0\ud3ec\uc2a4\uc640 \ud5f7\uac08\ub9ac\uc9c0 \ub9d0 \uac83.
    \n
    \n [\ubcf8\ubb38\uc73c\ub85c]
    \n <\/a>\n<\/li>\n
  2. \n \uc6d0\ub798 \uadf8\uac74 \ub974\ubca1 \uc801\ubd84\ub860\uc744 \uc880 \uacf5\ubd80\ud574\ubd10\uc57c \ud558\ub294\ub370 \uc0ac\uc2e4 \ub098\ub3c4 \uacf5\ubd80\ub97c \ud55c\uc9c0 \uc624\ub798\ub418\uc5b4 \uc0c8\ub85c \uacf5\ubd80\ud574\uc57c \ud55c\ub2e4.
    \n
    \n [\ubcf8\ubb38\uc73c\ub85c]
    \n <\/a>\n<\/li>\n<\/ol>\n<\/div>\n