¡¡¤³¤Î¾Ï¤Ç¤Ïγ»Ò¤¬¥Ý¥Æ¥ó¥·¥ã¥ë¥¨¥Í¥ë¥®¡¼1/2kx2¤Çɽ¤µ¤ì¤Æ¤¤¤ë¤è¤¦¤Ê¥Ý¥Æ¥ó
¥·¥ã¥ëÆâ¤Ë¸ºß¤·¤Æ¤¤¤ë¾ì¹ç¤Ë¤Ä¤¤¤Æ²ò¤¯¡£¸ÅŵŪ¤Ë¹Í¤¨¤ë¤Ê¤é¤Ð¤³¤ì¤Ï¤Ð¤Í¤Ë¤Ä¤Ê¤¬¤ì¤¿Î³»Ò¤Î±¿Æ°¤Ç¤¢¤ë¡£¡Ö¤Ð¤Í¤Ë¤Ä¤Ê¤¬¤ì¤¿ÎÌ»ÒÎϳØÅªÎ³»Ò¤Ê¤ó¤Æ¤Ê¤¤¤«
¤é¡¢¤³¤ó¤ÊÌäÂê¤Ïñ¤Ê¤ëÎý½¬ÌäÂê¤Ç¤¢¤Ã¤Æ¡¢¸½¼ÂŪ¤ÊʪÍý¤È´Ø·¸¤Ê¤¤¤À¤í¤¦¡×¤Ê¤É¤È»×¤Ã¤Æ¤Ï¤¤¤±¤Ê¤¤¡£¤à¤·¤íµÕ¤Ë¡¢¸½¼ÂŪ¤ÊʪÍý¤Î¤¤¤í¤ó¤Ê¤È¤³¤í¤Ç¤³¤ÎÄ´ÏÂ
¿¶Æ°»Ò¤Ï´é¤ò½Ð¤¹¤Î¤Ç¤¢¤ë¡£¤È¤¤¤¦¤Î¤Ï¶á»÷Ū¤Ë¹Í¤¨¤ì¤Ð¿¤¯¤ÎÎϳطϤ¬Ê¿¹ÕÅÀ¤òÃæ¿´¤È¤·¤ÆÊѰ̤ËÈæÎ㤹¤ë¤è¤¦¤ÊÎϤò¼õ¤±¤Æ¤¤¤ëʪÂΤȹͤ¨¤ë¤³¤È¤¬¤Ç¤¤ë¤«
¤é¤Ç¤¢¤ë¡£¤¿¤È¤¨¤Ð¸ÇÂΤÎʬ»Ò¤ËȯÀ¸¤¹¤ë¿¶Æ°¤âÄ´Ï¿¶Æ°»Ò¤È¹Í¤¨¤Æ¤è¤¤¡£
¡¡¤Þ¤¿¡¢Åż§¾ì¤Ê¤É¡¢Ï¢Â³Åª¤Ë¶õ´Ö¤Ë³È¤¬¤Ã¤Æ¤¤¤ë¤è¤¦¤Ê·Ï¤â¡¢¥Õ¡¼¥ê¥¨ÊÑ´¹¤Ê¤É¤Îµ»Ë¡¤òÍѤ¤¤Æ¤¦¤Þ¤¯Ê¬²ò¤·¤Æ¤ä¤ë¤³¤È¤ÇÄ´Ï¿¶Æ°»Ò¤Î½¸¤Þ¤ê¤È¹Í¤¨¤ë¤³¤È¤¬
¤Ç¤¤ë¾ì¹ç¤¬Â¿¤¤¡£¤½¤â¤½¤âÎÌ»ÒÎϳؤλϤޤê¤Ï¥×¥é¥ó¥¯¤¬¸÷(Åż§¾ì)¤Î¥¨¥Í¥ë¥®¡¼¤ÎÊѲ½Î̤¬nh¦Í¤Î¤è¤¦¤Ëh¦Í¤ÎÀ°¿ôÇܤˡÖÎ̻Ҳ½¡×¤µ¤ì¤ë¤³¤È¤Ëµ¤¤Å¤¤
¤¿¤«¤é¤Ç¤¢¤Ã¤¿¡£°Ê²¼¤Ç¶ñÂÎŪ·×»»¤ò½Ò¤Ù¤ë¤¬¡¢nh¦Í¤Î¤è¤¦¤Ë¥¨¥Í¥ë¥®¡¼¤¬Î̻Ҳ½¤µ¤ì¤ë¤³¤È¤Ï¤Þ¤µ¤ËÄ´Ï¿¶Æ°»Ò¤ÎÆÃħ¤Ç¤¢¤ë¡£¤Ä¤Þ¤êÄ´Ï¿¶Æ°»Ò¤ÏºÇ½é¤Ë¸«
ÉÕ¤±¤é¤ì¤¿ÎÌ»ÒÎϳØÅª·Ï¤Ç¤¢¤ë¤È¤â¸À¤¨¤ë¡£ÍýÏÀŪ¤Ë¤â±þÍÑŪ¤Ë¤â¡¢Ä´Ï¿¶Æ°»Ò¤ÎÎÌ»ÒÎϳؤÏÈó¾ï¤Ë½ÅÍפʤΤǤ¢¤ë¡£
|
(15.1) |
|
(15.2) |
|
(15.3) |
¦Ø
¤Ç³ä¤Ã¤Æ±¦Êդη¸¿ô¤ò̵¼¡¸µ²½¤¹¤ë¡Ê¤Ê¤¼
¦Ø¤ò»È¤¦¤Î¤«¤Ë¤Ä¤¤¤Æ¤Ï¡¢²¼¤ÎÌ䤤¤ò»²¾È¡Ë¡£
|
(15.4) |
/m¦Ø]},E=(¦Ë+1/2)
¦Ø ¤È¤·¤Æ¤ª¤¯79¤È·¸¿ô¤¬´Êñ¤Ë¤Ê¤Ã¤Æ
|
(15.5) |
¤äm¤ä¦Ø¤Ê¤É¡¢¼¡¸µ¤ò»ý¤Ã¤¿Äê¿ô¤ò¤¹¤Ù¤Æ1¤À
¤È¤¹¤ë¡Ê¤³¤ì¤é¤¬1¤Ë¤Ê¤ë¤è¤¦¤Êñ°Ì·Ï¤ò»È¤Ã¤ÆÌäÂê¤ò²ò¤¯¡Ë¡×¤ÈƱ¤¸¤³¤È¤Ê¤Î¤Ç¡¢(15.2)¤ò¸«¤Æ¡¢
¡Ö¤Ï¤¤¡¢º£¤«¤é
¤Èm
¤È¦Ø¤¬1¤Ë¤Ê¤ë¤è¤¦¤Êñ°Ì·Ï¤Ç·×»»¤·¤Þ¤¹¤è¡ª¡×¤ÈÀë¸À¤·¤Æ¡¢¤¹¤°¤Ë(15.5)¤ò½ñ¤²¼¤·¤Æ¤â¤è¤¤¡Ê·×»»
¤È¤·¤Æ¤Ï¤â¤Á¤í¤ó¤³¤Ã¤Á¤ÎÊý¤¬³Ú¤Ç¤¢¤ë¡Ë¡£
¡¡¡Ö¤³¤ó¤Ê¤Õ¤¦¤Ë¤Ê¤ó¤Ç¤â¤«¤ó¤Ç¤â1¤Ë¤·¤Æ¤·¤Þ¤Ã¤Æ¡¢¸å¤Ç¬ÄêÃͤÈÈæ³Ó¤¹¤ë»þ¤Ëº¤¤é¤Ê¤¤¤Î¤À¤í¤¦¤«¡©¡×¤ÈÉ԰¤ˤʤ뤫¤â¤·¤ì¤Ê¤¤¤¬¡¢¼¡¸µ¤Î¤¢¤ë¸µ¤Îñ°Ì·Ï
¤Ë¤Á¤ã¤ó¤ÈÌá¤Ã¤Æ¤³¤ì¤ë¤Î¤Ç¿´ÇÛ¤¹¤ëɬÍפϤʤ¤¡£º£¡¢¡ÖŤµ¡×¡Ö»þ´Ö¡×¡Ö¼ÁÎ̡פȣ³¤Ä¤Î¼¡¸µ¤¬¤¢¤ê¡¢1¤Ë¤·¤Æ¤·¤Þ¤Ã¤¿Äê¿ô¤â
,m,¦Ø¤È£³¤Ä¤¢¤ë¡£
¤·¤«¤â¡¢¤³¤Î£³¤Ä¤ÎÄê¿ô¤Î¼¡¸µ¤ÏÆÈΩ¤Ç¤¢¤ê¡¢Ä¹¤µ¤Î¼¡¸µ¤ò£²Ä̤ê¤ÎÊýË¡¤Çºî¤ì¤¿¤ê¤Ï¤·¤Ê¤¤¡£¤³¤Î¤è¤¦¤Ê¾ì¹ç¡¢¸å¤Ç¡Ö¼¡¸µ¤¬¤¢¤¦¤è¤¦¤ËÄê¿ô¤ÎÁȤ߹ç¤ï¤»¤ò¤«
¤±¤ë¡×¤È¤¤¤¦ºî¶È¤ò¤ä¤Ã¤Æ¤ä¤ì¤Ð¡¢Ä̾ï¤Îñ°Ì·Ï¤Ç¤Îɽ¸½¤ËÌá¤ë¡£¤¿¤È¤¨¤Ð̵¼¡¸µ²½¤·¤¿¸å¥¨¥Í¥ë¥®¡¼¤ò·×»»¤·¤Æ1.5¤È¤¤¤¦Åú¤¨¤¬½Ð¤¿¤Î¤Ç¤¢¤ì¤Ð¡¢¤³¤ì¤Ë
¦Ø¤ò¤«¤±¤Æ1.5
¦Ø¤È¤·¤¿¤â¤Î¤¬¼¡¸µ¤Î
¤¢¤ëñ°Ì·Ï¤Ç¤Î¥¨¥Í¥ë¥®¡¼¤Ç¤¢¤ë¡£
,m,¦Ø¤ò»È¤Ã¤Æ¥¨¥Í¥ë¥®¡¼¤Î¼¡¸µ¤ÎÎ̤òºî¤í¤¦¤È¤¹¤ë¤È¡¢
¦Ø°Ê³°¤Ë¤Ê¤¤¤³¤È¤Ï¤¹¤°¤Ë¤ï¤«¤ë¡£
|
)]¤Ç¤¢¤Ã¤¿¡£¤³¤Î»þ¤ÏV¤¬Äê¿ô¤Ç¤¢¤Ã¤¿¤¬¡¢º£¤ÏV=1/2m¦Ø2x2¤Èx
¤Î´Ø¿ô¤Ë¤Ê¤Ã¤Æ¤¤¤ë¡£Äê¿ô¦Ê¤ËÂФ·¤Æexp¤Î¸ª¤¬¡Ý¦Êx¤È¤Ê¤Ã¤¿¤Î¤À¤«¤é¡¢¦Ê¤¬x¤Î´Ø¿ô¦Ê(x)¤È¤Ê¤ì¤Ð¡¢exp ¤Î¸ª¤Ï¡Ý¢é¦Ê(x)dx¡¢¤¹¤Ê¤ï¤Á
|
(15.6) |
|
(15.7) |
|
(15.8) |
|
(15.9) |
¦Ø¤Î»þ¤Î²ò¤Ë¤Ê¤Ã¤Æ¤¤¤ë¤³¤È¤¬¤ï¤«¤ë¡£¤³¤ì¤Ç
¤È¤ê¤¢¤¨¤º¡¢°ì¤Ä¤Î²ò
|
(15.10) |
¦Ø¤Ç¤¢¤ë¡£¼Â¤Ï¤³¤ì¤¬²ò¤ÎÃæ¤Ç¤ÏºÇÄã¤Î¥¨¥Í¥ë¥®¡¼¸ÇÍÃͤò»ý¤Ä¤â¤Î¤Ç¡¢´ðÄì¾õ
ÂÖ¤ÎÇÈÆ°´Ø¿ô¤Ç¤¢¤ë¡£
|
(15.11) |
|
(15.12) |
¦Ø¤Î»þ°Ê³°¤Ç¤â¡¢²ò¤Ï±óÊý¤Ç¤Ïe¡Ý1/2¦Î2¤Î
·Á¤Ë¤Ê¤ë¤È¹Í¤¨¤é¤ì¤ë¤Î¤Ç¡¢
|
(15.13) |
|
(15.14) |
|
|
(15.15) |
|
(15.16) |
|
(15.17) |
|
(15.18) |
|
(15.19) |
|
(15.20) |
|
(15.21) |
|
|
(15.27) |
¦Ø¤ò»ý¤ÄÇÈ
ư´Ø¿ô¤È¥¨¥Í¥ë¥®¡¼(n+1/2)
¦Ø¤ò»ý¤ÄÇÈ
ư´Ø¿ô¤ÎÆâÀѤÏ
|
(15.28) |
¦Ø¤ò¤«¤±¤ë¤À¤±¤Ç¤¤¤¤¤Î¤Ç¤¹¤«¡©
,¦Ø¤ò£±¤Ë¤¹¤ë¤È1¤Ë¤Ê¤ë¼°¡Ë¤È¤¤¤¦·Á¤Ë¤Ê¤Ã¤¿¤Ï¤º¤Ç¤¹¡£¤½¤·¤Æ¡¢¡Êm,
,¦Ø¤ò£±¤Ë¤¹¤ë¤È1¤Ë¤Ê¤ë¼°¡Ë¤Ç¥¨¥Í¥ë¥®¡¼¤Î¼¡¸µ¤ò»ý¤Ä¤Î¤Ï
¦Ø¤·¤«¤Ê¤¤¤ï¤±¤Ç¤¹¡£