[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/296385#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/296385","headline":"\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9 – Wikipedia","name":"\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9 – Wikipedia","description":"3\u6b21\u5143\u56fa\u4f53\u3067\u306e\u72b6\u614b\u5bc6\u5ea6g(E) vs \u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u56f3\u3002\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u306fdg(E)\/dE\u304c\u767a\u6563\u3059\u308b\u70b9\u3067\u8d77\u3053\u308b\u3002 \u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u3068\u306f\u7d50\u6676\u306e\u72b6\u614b\u5bc6\u5ea6\uff08DOS\uff09\u3067\u307f\u3089\u308c\u308b\u7279\u7570\u70b9\uff08\u6ed1\u3089\u304b\u3067\u306a\u3044\u70b9\uff09\u306e\u3053\u3068\u3002 \u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u304c\u751f\u3058\u308b\u6ce2\u6570\u30d9\u30af\u30c8\u30eb\u306f\u3001\u30d6\u30ea\u30eb\u30a2\u30f3\u30be\u30fc\u30f3\u306e\u81e8\u754c\u70b9\u3068\u547c\u3070\u308c\u308b\u3002 3\u6b21\u5143\u7d50\u6676\u306e\u5834\u5408\u3001\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u306f\u30ad\u30f3\u30af\u3068\u306a\u308a\u3001\u305d\u3053\u3067\u306f\u72b6\u614b\u5bc6\u5ea6\u304c\u5fae\u5206\u53ef\u80fd\u3067\u306a\u304f\u306a\u308b\u3002 \u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u306e\u6700\u3082\u4e00\u822c\u7684\u306a\u5fdc\u7528\u306f\u3001\u5149\u5438\u53ce\u30b9\u30da\u30af\u30c8\u30eb\u306e\u89e3\u6790\u3067\u3042\u308b\u3002 \u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u306f\u30011953\u5e74\u306b\u30d9\u30eb\u30ae\u30fc\u306e\u7269\u7406\u5b66\u8005\u30ec\u30aa\u30f3\u30fb\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u304c\u30d5\u30a9\u30ce\u30f3\u306e\u72b6\u614b\u5bc6\u5ea6\u306b\u3064\u3044\u3066\u6700\u521d\u306b\u53d6\u308a\u6271\u3063\u305f\u3002 [1] N\u7c92\u5b50\u30b5\u30a4\u30c8\u304b\u3089\u306a\u308b1\u6b21\u5143\u683c\u5b50\u3092\u8003\u3048\u308b\u3002 \u5404\u7c92\u5b50\u30b5\u30a4\u30c8\u9593\u306e\u8ddd\u96e2\u306fa\u3067\u3001\u5168\u9577\u306fL = Na\u3068\u3059\u308b\u3002 \u3053\u3053\u3067\u3001\u3053\u306e1\u6b21\u5143\u306e\u7bb1\u306e\u4e2d\u306b\u5b9a\u5728\u6ce2\u304c\u3042\u308b\u3068\u4eee\u5b9a\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u5468\u671f\u7684\u5883\u754c\u6761\u4ef6\u3092\u7528\u3044\u308b\u306e\u304c\u4fbf\u5229\u3067\u3042\u308b\u3002 [2] k=2\u03c0\u03bb=n2\u03c0L{displaystyle k={frac {2pi }{lambda }}=n{frac","datePublished":"2022-04-27","dateModified":"2022-04-27","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/cd810e53c1408c38cc766bc14e7ce26a?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/c\/c7\/NewvanHove.png\/220px-NewvanHove.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/c\/c7\/NewvanHove.png\/220px-NewvanHove.png","height":"170","width":"220"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/296385","about":["wiki"],"wordCount":5217,"articleBody":"  3\u6b21\u5143\u56fa\u4f53\u3067\u306e\u72b6\u614b\u5bc6\u5ea6g(E) vs \u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u56f3\u3002\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u306fdg(E)\/dE\u304c\u767a\u6563\u3059\u308b\u70b9\u3067\u8d77\u3053\u308b\u3002\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u3068\u306f\u7d50\u6676\u306e\u72b6\u614b\u5bc6\u5ea6\uff08DOS\uff09\u3067\u307f\u3089\u308c\u308b\u7279\u7570\u70b9\uff08\u6ed1\u3089\u304b\u3067\u306a\u3044\u70b9\uff09\u306e\u3053\u3068\u3002  \u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u304c\u751f\u3058\u308b\u6ce2\u6570\u30d9\u30af\u30c8\u30eb\u306f\u3001\u30d6\u30ea\u30eb\u30a2\u30f3\u30be\u30fc\u30f3\u306e\u81e8\u754c\u70b9\u3068\u547c\u3070\u308c\u308b\u30023\u6b21\u5143\u7d50\u6676\u306e\u5834\u5408\u3001\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u306f\u30ad\u30f3\u30af\u3068\u306a\u308a\u3001\u305d\u3053\u3067\u306f\u72b6\u614b\u5bc6\u5ea6\u304c\u5fae\u5206\u53ef\u80fd\u3067\u306a\u304f\u306a\u308b\u3002\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u306e\u6700\u3082\u4e00\u822c\u7684\u306a\u5fdc\u7528\u306f\u3001\u5149\u5438\u53ce\u30b9\u30da\u30af\u30c8\u30eb\u306e\u89e3\u6790\u3067\u3042\u308b\u3002\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u306f\u30011953\u5e74\u306b\u30d9\u30eb\u30ae\u30fc\u306e\u7269\u7406\u5b66\u8005\u30ec\u30aa\u30f3\u30fb\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u304c\u30d5\u30a9\u30ce\u30f3\u306e\u72b6\u614b\u5bc6\u5ea6\u306b\u3064\u3044\u3066\u6700\u521d\u306b\u53d6\u308a\u6271\u3063\u305f\u3002[1]  N\u7c92\u5b50\u30b5\u30a4\u30c8\u304b\u3089\u306a\u308b1\u6b21\u5143\u683c\u5b50\u3092\u8003\u3048\u308b\u3002\u5404\u7c92\u5b50\u30b5\u30a4\u30c8\u9593\u306e\u8ddd\u96e2\u306fa\u3067\u3001\u5168\u9577\u306fL = Na\u3068\u3059\u308b\u3002\u3053\u3053\u3067\u3001\u3053\u306e1\u6b21\u5143\u306e\u7bb1\u306e\u4e2d\u306b\u5b9a\u5728\u6ce2\u304c\u3042\u308b\u3068\u4eee\u5b9a\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u5468\u671f\u7684\u5883\u754c\u6761\u4ef6\u3092\u7528\u3044\u308b\u306e\u304c\u4fbf\u5229\u3067\u3042\u308b\u3002[2]k=2\u03c0\u03bb=n2\u03c0L{displaystyle k={frac {2pi }{lambda }}=n{frac {2pi }{L}}}\u3053\u3053\u3067\u03bb{displaystyle lambda }\u306f\u6ce2\u9577\u3001n\u306f\u6574\u6570\u3067\u3042\u308b\u3002\u6b63\u306e\u6574\u6570\u306f\u524d\u9032\u3059\u308b\u6ce2\u3001\u8ca0\u306e\u6574\u6570\u306f\u5f8c\u9032\u3059\u308b\u6ce2\u3092\u8868\u3059\u3002  \u3053\u306e\u683c\u5b50\u4e2d\u306e\u6ce2\u52d5\u306e\u6ce2\u9577\u306f\u6700\u77ed\u30672a\u3067\u3042\u308a\u3001\u3053\u306e\u3068\u304d\u6700\u5927\u306e\u6ce2\u6570kmax=\u03c0\/a{displaystyle k_{max}=pi \/a}\u3068\u306a\u308a\u3001|n|\u306f\u6700\u5927\u5024nmax=L\/2a{displaystyle n_{max}=L\/2a}\u3068\u306a\u308b\u3002\u72b6\u614b\u5bc6\u5ea6g(k)dk\u3092\u3001\u6ce2\u6570\u30d9\u30af\u30c8\u30eb\u304ck\u304b\u3089k+dk\u3067\u3042\u308b\u5b9a\u5728\u6ce2\u306e\u6570\u3068\u3057\u3066\u5b9a\u7fa9\u3059\u308b\u3002[3]g(k)dk=dn=L2\u03c0dk{displaystyle g(k)dk=dn={frac {L}{2pi }},dk}3\u6b21\u5143\u306b\u62e1\u5f35\u3059\u308b\u3068\u3001\u7bb1\u306e\u4e2d\u306e\u72b6\u614b\u5bc6\u5ea6\u306f\u3001g(k\u2192)d3k=d3n=L3(2\u03c0)3d3k{displaystyle g({vec {k}})d^{3}k=d^{3}n={frac {L^{3}}{(2pi )^{3}}},d^{3}k}\u3053\u3053\u3067d3k{displaystyle d^{3}k}\u306fk\u7a7a\u9593\u3067\u306e\u4f53\u7a4d\u8981\u7d20\u3067\u3042\u308b\u3002\u307e\u305f\u96fb\u5b50\u3067\u306f2\u3064\u30b9\u30d4\u30f3\u306e\u65b9\u5411\u3092\u8003\u616e\u3057\u3066\u3001\u56e0\u5b50\uff12\u3092\u639b\u3051\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u9023\u9396\u5f8b\u306b\u3088\u308a\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u7a7a\u9593\u3067\u306eDOS\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u305b\u308b\u3002dE=\u2202E\u2202kxdkx+\u2202E\u2202kydky+\u2202E\u2202kzdkz=\u2207\u2192E\u22c5dk\u2192{displaystyle dE={frac {partial E}{partial k_{x}}}dk_{x}+{frac {partial E}{partial k_{y}}}dk_{y}+{frac {partial E}{partial k_{z}}}dk_{z}={vec {nabla }}Ecdot d{vec {k}}}\u3053\u3053\u3067\u2207\u2192{displaystyle {vec {nabla }}}\u306fk\u7a7a\u9593\u3067\u306e\u52fe\u914d\u3067\u3042\u308b\u3002k\u7a7a\u9593\u3067\u306e\u4f4d\u7f6e\u306e\u7d44\uff08\u7c92\u5b50\u30a8\u30cd\u30eb\u30ae\u30fcE\u306b\u5bfe\u5fdc\uff09\u306fk\u7a7a\u9593\u3067\u9762\u3092\u4f5c\u308a\u3001E\u306e\u52fe\u914d\u306f\u3053\u306e\u9762\u306e\u5168\u3066\u306e\u70b9\u3068\u76f4\u4ea4\u3059\u308b\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308b\u3002[4]\u3053\u306e\u30a8\u30cd\u30eb\u30ae\u30fcE\u306b\u3064\u3044\u3066\u306e\u95a2\u6570\u3067\u3042\u308b\u72b6\u614b\u5bc6\u5ea6\u306f\u3001g(E)dE=\u222c\u2202Eg(k\u2192)d3k=L3(2\u03c0)3\u222c\u2202Edkxdkydkz{displaystyle g(E)dE=iint _{partial E}g({vec {k}}),d^{3}k={frac {L^{3}}{(2pi )^{3}}}iint _{partial E}dk_{x},dk_{y},dk_{z}}\u3053\u3053\u3067\u7a4d\u5206\u306f\u5b9a\u6570E\u306e\u9762\u2202E{displaystyle partial E}\u306b\u308f\u305f\u308a\u884c\u3046\u3002kz\u2032{displaystyle k’_{z},}\u304c\u9762\u306b\u76f4\u4ea4\u3057\u3001E\u306e\u52fe\u914d\u306b\u5e73\u884c\u3068\u306a\u308b\u3088\u3046\u306a\u65b0\u3057\u3044\u5ea7\u6a19\u7cfbkx\u2032,ky\u2032,kz\u2032{displaystyle k’_{x},k’_{y},k’_{z},}\u3092\u9078\u3076\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u306e\u5ea7\u6a19\u7cfb\u304c\u5143\u306e\u5ea7\u6a19\u7cfb\u306e\u56de\u8ee2\u3067\u3042\u308c\u3070\u3001k’\u7a7a\u9593\u306e\u4f53\u7a4d\u8981\u7d20\u306f\u3001dkx\u2032dky\u2032dkz\u2032=dkxdkydkz{displaystyle dk’_{x},dk’_{y},dk’_{z}=dk_{x},dk_{y},dk_{z}}dE\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002dE=|\u2207\u2192E|dkz\u2032{displaystyle dE=|{vec {nabla }}E|,dk’_{z}}g(E)\u306e\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\u3001g(E)=L3(2\u03c0)3\u222cdkx\u2032dky\u2032|\u2207\u2192E|{displaystyle g(E)={frac {L^{3}}{(2pi )^{3}}}iint {frac {dk’_{x},dk’_{y}}{|{vec {nabla }}E|}}}\u3053\u3053\u3067dkx\u2032dky\u2032{displaystyle dk’_{x},dk’_{y}}\u9805\u306f\u3001\u5b9aE\u9762\u306e\u9762\u7a4d\u8981\u7d20\u3067\u3042\u308b\u3002g(E){displaystyle g(E)}\u306e\u5f0f\u306f\u3001\u5206\u6563\u95a2\u4fc2E(k\u2192){displaystyle E({vec {k}})}\u304c\u6975\u5024\u3068\u306a\u308bk{displaystyle k}\u70b9\u3067DOS\u306e\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u3002\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u306f\u3053\u308c\u3089\u306ek{displaystyle k}\u70b9\u3067\u306eDOS\u95a2\u6570\u3067\u8d77\u3053\u308b\u6027\u8cea\u3067\u3042\u308b\u3002\u8a73\u7d30\u306a\u89e3\u6790[5]\u306b\u3088\u308b\u3068\u30013\u6b21\u5143\u7a7a\u9593\u3067\u306f\u30d0\u30f3\u30c9\u69cb\u9020\u304c\u6975\u5927\u304b\u3001\u6975\u5c0f\u304b\u3001\u307e\u305f\u306f\u978d\u70b9\u304b\u306b\u4f9d\u5b58\u3057\u30664\u7a2e\u985e\u306e\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u304c\u3042\u308b\u30023\u6b21\u5143\u3067\u306fDOS\u306e\u5fae\u5206\u304c\u767a\u6563\u3057\u3066\u3082DOS\u81ea\u8eab\u306f\u767a\u6563\u3057\u306a\u3044\u3002\u95a2\u6570g(E)\u306f\u5e73\u65b9\u6839\u7279\u7570\u6027\uff08\u56f3\u3092\u53c2\u7167\uff09\u3092\u3082\u3064\u50be\u5411\u306b\u3042\u308b\u3002\u81ea\u7531\u96fb\u5b50\u306e\u30d5\u30a7\u30eb\u30df\u9762\u3067\u306f\u3001E=\u210f2k2\/2m{displaystyle E=hbar ^{2}k^{2}\/2m}|\u2207\u2192E|=\u210f2k\/m=\u210f2Em{displaystyle |{vec {nabla }}E|=hbar ^{2}k\/m=hbar {sqrt {frac {2E}{m}}}}.2\u6b21\u5143\u3067\u306eDOS\u306f\u978d\u70b9\u3067\u5bfe\u6570\u7684\u306b\u767a\u6563\u3057\u30011\u6b21\u5143\u3067\u306eDOS\u306f\u2207\u2192E{displaystyle {vec {nabla }}E}\u304c\u30bc\u30ed\u3068\u306a\u308b\u3068\u3053\u308d\u3067\u7121\u9650\u3068\u306a\u308b\u3002\u56fa\u4f53\u306e\u5149\u5438\u53ce\u30b9\u30da\u30af\u30c8\u30eb\u306f\u3001\u30d0\u30f3\u30c9\u69cb\u9020\u304b\u3089\u30d5\u30a7\u30eb\u30df\u306e\u9ec4\u91d1\u5f8b\u3092\u7528\u3044\u3066\u8a08\u7b97\u3055\u308c\u308b\u3002\u305d\u3053\u3067\u8a55\u4fa1\u3055\u308c\u308b\u884c\u5217\u8981\u7d20\u306f\u53cc\u6975\u5b50\u6f14\u7b97\u5b50A\u2192\u22c5p\u2192{displaystyle {vec {A}}cdot {vec {p}}}\u3067\u3042\u308b\u3002\u3053\u3053\u3067A\u2192{displaystyle {vec {A}}}\u306f\u30d9\u30af\u30c8\u30eb\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3001p\u2192{displaystyle {vec {p}}}\u306f\u904b\u52d5\u91cf\u6f14\u7b97\u5b50\u3067\u3042\u308b\u3002\u30d5\u30a7\u30eb\u30df\u306e\u9ec4\u91d1\u5f8b\u3067\u73fe\u308c\u308b\u72b6\u614b\u5bc6\u5ea6\u306f\u7d50\u5408\u72b6\u614b\u5bc6\u5ea6\uff08JDOS\uff09\u3067\u3001\u4e0e\u3048\u3089\u308c\u305f\u5149\u5b50\u30a8\u30cd\u30eb\u30ae\u30fc\u3067\u5206\u96e2\u3055\u308c\u308b\u4f1d\u5c0e\u5e2f\u3068\u4fa1\u96fb\u5b50\u5e2f\u3067\u306e\u96fb\u5b50\u72b6\u614b\u306e\u6570\u3067\u3042\u308b\u3002\u5149\u5438\u53ce\u306f\u3001\u53cc\u6975\u5b50\u6f14\u7b97\u5b50\u306e\u884c\u5217\u8981\u7d20\uff08\u632f\u52d5\u5b50\u5f37\u5ea6\uff09\u3068JDOS\u306e\u7a4d\u306b\u3088\u308b\u3082\u306e\u3067\u3042\u308b\u30022\u6b21\u5143\u30681\u6b21\u5143\u3067\u306eDOS\u306e\u767a\u6563\u306f\u6570\u5b66\u7684\u306b\u4e88\u60f3\u3055\u308c\u3066\u304a\u308a\u3001\u5bb9\u6613\u306b\u89b3\u6e2c\u3067\u304d\u308b\u3002\u30b0\u30e9\u30d5\u30a1\u30a4\u30c8\uff08\u64ec\uff12\u6b21\u5143\uff09\u3084Bechgaard\u5869\uff08\u64ec1\u6b21\u5143\uff09\u306e\u3088\u3046\u306a\u7570\u65b9\u6027\u56fa\u4f53\u3067\u306f\u3001\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u306b\u3088\u308b\u30b9\u30da\u30af\u30c8\u30eb\u306e\u7570\u5e38\u304c\u307f\u3089\u308c\u308b\u3002\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u306f\u64ec1\u6b21\u5143\u7cfb\u3067\u3042\u308b\u5358\u5c64\u30ab\u30fc\u30dc\u30f3\u30ca\u30ce\u30c1\u30e5\u30fc\u30d6\uff08SWNT\uff09\u306e\u5149\u5f37\u5ea6\u3067\u91cd\u8981\u3068\u306a\u308b\u3002\u30b0\u30e9\u30d5\u30a7\u30f3\u306e\u30c7\u30a3\u30e9\u30c3\u30af\u70b9\u306f\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u3067\u3042\u308a\u3001\u30b0\u30e9\u30d5\u30a7\u30f3\u304c\u96fb\u6c17\u7684\u4e2d\u6027\u306e\u3068\u304d\u306e\u96fb\u6c17\u62b5\u6297\u306e\u30d4\u30fc\u30af\u3068\u3057\u3066\u89b3\u6e2c\u3055\u308c\u308b\u3002\u306d\u3058\u308c\u305f\u30b0\u30e9\u30d5\u30a7\u30f3\u5c64\u3082\u3001\u5c64\u9593\u306e\u30ab\u30c3\u30d7\u30ea\u30f3\u30b0\u306b\u3088\u308b\u72b6\u614b\u5bc6\u5ea6\u306e\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9\u3092\u793a\u3059[6]\u3002\u53c2\u8003\u6587\u732e[\u7de8\u96c6]^ L. Van Hove, “The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal,” Phys. Rev. 89, 1189\u20131193 (1953).^ See equation 2.9 in http:\/\/www2.physics.ox.ac.uk\/sites\/default\/files\/BandMT_02.pdf From \u03d5(x+L)=\u03d5(x){displaystyle phi (x+L)=phi (x)} we have kL=2n\u03c0{displaystyle kL=2npi }^ *M. A. Parker(1997-2004)“Introduction to Density of States” Marcel-Dekker Publishing p.7.   Archived September 8, 2006, at the Wayback Machine.^ *Ziman, John (1972). Principles of the Theory of Solids. Cambridge University Press. ISBN B0000EG9UB\u00a0^ *Bassani, F.; Pastori Parravicini, G. (1975). Electronic States and Optical Transitions in Solids. Pergamon Press. ISBN\u00a00-08-016846-9\u00a0 This book contains an extensive discussion of the types of Van Hove singularities in different dimensions and illustrates the concepts with detailed theoretical-versus-experimental comparisons for Ge and graphite.^ I. Brihuega et al., Physical Review Letters 109, 196802 (2012)."},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki27\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki27\/archives\/296385#breadcrumbitem","name":"\u30d5\u30a1\u30f3\u30fb\u30db\u30fc\u30d9\u7279\u7570\u70b9 – Wikipedia"}}]}]