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  • 2022-06-09
    [color=#000000]设石原子[/color][color=#000000]([/color][color=#000000]原子序数为[/color][color=#000000] 5)[/color][color=#000000]受到[/color][color=#000000] [tex=4.643x1.571]QtA0Z04GgW4d1d+cV/x2rJcJSP3V3CCM8e1ngH6ijMs=[/tex] [/color][color=#000000]的微扰作[/color][color=#000000]用[/color][color=#000000], [/color][color=#000000]在一级近似下[/color][color=#000000](1) [/color][color=#000000]问价电子[/color][color=#000000] [tex=1.071x1.214]QNlCeTWiPvK4dPwBORP+PQ==[/tex] [/color][color=#000000]能级分裂成几个能级[/color][color=#000000]?[/color][color=#000000](2) [/color][color=#000000]如已知其中一个能级的移动值[/color][color=#000000] [tex=2.929x1.214]aFoSwDPjVd7cTUYeJ81ijw==[/tex] [/color][color=#000000]求其余各能级的移[/color][color=#000000]动值[/color][color=#000000];[/color][color=#000000](3) [/color][color=#000000]求出各能级对应的波函数[/color][color=#000000],[/color][color=#000000]用原来的[/color][color=#000000] [tex=1.071x1.214]QNlCeTWiPvK4dPwBORP+PQ==[/tex] [/color][color=#000000]态波函数[/color][color=#000000] [tex=2.0x1.214]TY2Tx7PgpuxXipzxqjeI8w==[/tex] [tex=1.714x1.214]jsDx3GX2uz/6I1rBxD/OHQ==[/tex] [color=#000000] [/color][color=#000000]与[/color][color=#000000] [tex=2.286x1.214]m58aVZf+YcSq9yq11/Kpig==[/tex][/color][color=#000000]表示[/color][color=#000000]. [/color][/color]
    • [color=#000000]解[/color][color=#000000]: (1) [/color][color=#000000]未受微扰时[/color][color=#000000], [tex=1.071x1.214]QNlCeTWiPvK4dPwBORP+PQ==[/tex] [/color][color=#000000]电子能级对应如下三个波函数[/color][color=#000000][tex=20.214x1.5]ZGcG0dzbmc8mgoaR9o421G0n5siMxKa3PcfvqyCdPYY8nbi3gkzUWIYGMOhAxiHGKwEerNv46TjXq38GncfrjwLAGVz4C5eAd5p4bs0YfGkdy1F2Nw4eB11H1S74Lwx1NX7EHCFeu+B9NqtGp9A9E6uvkXC2Yj8oDywY40azZBM=[/tex] 不含[/color][color=#000000] [tex=14.643x1.5]NUYPx3z0VghxM1nlreVREba01cMbV8D0GtkMI1Gw0foCOoHl+JbC9EjFPZuMbHgdX3nWABkLhCzwSEOIwsc2d7zJj3RotAVDUN9ZvRNq5wtg9B4OJWSMd1k+zfBJ3YTN[/tex][/color][color=#000000]令零级近似波函数为[/color][tex=11.643x1.571]LljuTf9rAVQ/d82XBnXv3tHl/euPAuWLegOzauWJ82E+5yRbBsqcGAmTjxjo80yx1e9CBilySxhxylA8cTLXyZmqX97V5gpnS9f/1uGIl1s=[/tex][color=#000000]系数[/color][color=#000000] [tex=2.357x1.0]UGs/m/TxQmhHsmQOGjDkXNWKwLcoBCSwqBeGHaNqe30=[/tex] [/color][color=#000000]满足方程[/color][tex=24.143x5.214]De166nmeTkb4C/83+ZZH22a8UEqsDN2wHcGlVfOobr7CBB1339rNO2tO1lPptqp3jVRyKQYRWYLkmikMgp3mepcDUgyhZ2b0iCjJH1UCtIiI662ALbTasqXw98lYN7oMLhcPnrsMiEP9SqYlDxvB3uqL5WuVbre4jgUbtOrXLitN1H0l3Dtz0RsaGQpWPSKCYlnhIls/jgkxJIU5BTpXyf3VyODWNCSbw8ZtYGw6fZerHV28wPjD8QtEpn/RwFg2lIu8kiZMykc2yOusLWYkh1kwGpGw7kef3CBfZQVvZG8XTtoCN9zXh4AL5LWcyXupvioFA7ANqCf/XS8xN6j2M4IJxvux06dMFvdISqFvpol56JiKg9XT73krwyHFoggwYrBHhlmM9gG0tPpaqr/kXfvNVsN35t10cRVSUPeGuteTLgHhgWSejKmOFiDi7OyJ[/tex][color=#000000]其中[/color][color=#000000] [tex=17.071x2.643]Hd94xy7h2R1k1hh0RT0sep29FC0O69i1zo3ud7nlyYe297gz5/D2Mxq8b3WSE/TwJPu6eDoE8P1rDT4gbT4sl0BE8bYs30jGCScBrOXehz9jnWx327lPQmyt1GqAm+TQLBXHIDV2VgIh1Nd8P7tT5Q==[/tex][/color][color=#000000]将[/color][color=#000000] [tex=26.643x2.5]GnpNe1KXEag56bnOPMYGKFNzzwC7IaRcg9izwXXEhwssoFnDSM8+btWF6eQG2zB8hAXqFbJV1AO5ONdDPJUpwOUIUkL0uwbpXrrPD8J2mhOI1rqIADJz/KGbcEo+FjwlGwvNbKP6jHZp3ZsACU8nXw6jzG1dcYewZuIXkcDJoconl001gCYq1uRI9/D/1PzSK2AeHFW4W83yu+dyY8ktadUxTfhShW1iJGCr9A5JOaVEDF9iw3+tb4obuXQdh4vqW4E9MjATTBp+wXsALBr7wg==[/tex] [/color][color=#000000]代入[/color][color=#000000] (4) [/color][color=#000000]式[/color][color=#000000], [/color][color=#000000]得[/color][tex=25.357x8.929]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[/tex][tex=20.143x1.429]SLBB4lxutjRzqfZe6Qp/tYM5GEZfgquxK6kmU2cziWimMRPb50PTWFMcfP3u83STOcPv2ieq6xqJDfLvxL1YVCUSJeIxPNuowYIl+b3zQ9Np7Dn3/CoCGgnktpnLbivBU8QynuaHoVRFZeKUD41ACRZkTXVUuN6oxn8OgpW7KZx+8Hw+OWOeck3mMr5PFZCo4vZtCZslOYj3Gw3yi1gB/A==[/tex][color=#000000]令 [tex=7.857x1.429]uNuO/CeUaFmsVR8npwnYmLaYCJ8i8iff+dP8PRv2vEev7odRXaG4OMeS1nMj/zOUmdAIeZPmthEeaumGlyCd1A==[/tex][/color][color=#000000] [/color][color=#000000]方程[/color][color=#000000](3)[/color][color=#000000]变为[/color][tex=19.571x4.643]rwMhqGKFQ+j3l2qMx/grPhf2QHhK1QKq6A/GG3tqQxHj9daXNB7ydoTTKo16lev8cE803A0lg9iTVxcd5ToLqSWgmvkrSsBbfg4sbqkPJ9/SSW8bo8VdddXjmlTyi47RtOnQ2UlNm5NBia8GXBT6inQkZ9uonY4MDOF/mCbJyKP2eDsUxpD5f0PhSwpW0RjdSoLGM9BUgu+GPwmqC7z8xf0okJNBfVgDctm3Iyd3BjMtPp0l8SnPkWQjUFrc1FQT[/tex][color=#000000]解之得[/color][tex=22.214x7.357]rZM5/OPAdr7aX+kNl9iwpDJ98u4aIZO4wWbGXarN4mpV1xueiCDQNb1FzE+TY9skzphbK9vhQh1jO2HbyOCU/Qm1SU9Hv8XHGULFAznJJA/eEz9MVCKS0QirgQDHIF/trCtnXSgIBQ3kGNLFW7oa2UG+4TxEBLFT6gGvWey4Uh0rIo+NVEtI/JptKXVEfahO9/I9MDud/P18NudDoI1qbe62n2X2KgsgnZi39kQ9+Xi/nv3pvnJ9P8CiE0WKEKWvdsCRsqtiFJF28WRzos+OcViMltU9VOIxG1ImmJ0PH83F87e0enLL7rwbG89EIiA047CrwPzovuZCoO5tFzbOOQ5KNygUlLCqm3z9U2Z3ThgkehJqkGdyOF9nHmdxPcaMP9Gl+t5h3Fyp6o9c2yv93oPfa5XT6u9NUHxhiHO/5q7522hnGR3N6K4wGZdhc/eR[/tex][tex=23.214x3.643]6AabqAMBXV/JTrRoP3MU5ZRc+Op2DgEQyv0La9Jy4/yXegDMipVMqXpCxR6BUd561iYx0JQMfVaIZxqwiH7Pxyvu2Ma8/VILwUEV2Ok1MGkbsTQ5jgNYH1DoEf+azNSgzQ9CqrmhIlQnFmsVs59LWbwlm3h27tg8FsrCaTjRaZH28Njk1X7wt9vizbkk1Kfofg7ZRkoy2PlEK2LEZvMRlJW47VssMCVxlCrDsL6KHEGo2340qc79hEVy63oC/McD[/tex][color=#000000][tex=1.357x1.357]1hVFm0IwVTij415W1ZtiYg==[/tex] 为能级移动值[/color][color=#000000],[/color][color=#000000]由题意知[/color][color=#000000], [tex=3.143x1.357]UN1nS/EHipysEpoID/3K8g==[/tex] [/color][color=#000000]可见，能级一分为三[/color][color=#000000]. [/color][color=#000000]这三个能级的能量和相应的波函数为[/color][tex=21.857x8.643]rZM5/OPAdr7aX+kNl9iwpMcDIWU9UxrXm/9v07CvUJABXXYjfLUBkHU4DcB21HSSnzCkLofLeceWu9fZE+itbFWA37AsqRrgRA08YkHQ/euDjZI7EUGzciDnMN/8cf+jw2HEIIUnDb6d8hSY6Nw5GBP0F5QFoFpmxyon0Fq2vieMzfE7Qa8DtrpkXymx7wr94dg8Laf0lYqdAfu9IaTmAeb+rM82wWZWFl2fphAYBTDmgQ9mvDPYgU+3TZePZVAlCvft4fqA1unhQppf/I/a833bJeKwpcMBDhChq/BESyCV7g4v1rUiA4Wu2+A0qP1s/ZWxjjeiJL0M06gojdZBkL/4QDVbRgmqMW5ZZuEZM0WOt17Hr5QKVYlJSS1GHBLy0DVEvKvEug0hSlNyhzPn/RZjNQSyaFdvgaqXK3A8fyLeGRRZjRwrjqxncrJ35UGF[/tex]
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    举一反三

    内容

    • 0

      [color=#000000]有一平行板空气电容器 [/color][color=#000000]，[/color][color=#000000]极板[/color][color=#000000]的面积均为[/color][tex=0.643x1.0]fYkALuFzYlFm0R716i1EGA==[/tex][color=#000000][/color][color=#000000]，[/color][color=#000000]极板间距为 [/color][color=#000000][tex=0.571x1.0]TcM6B5Wrs5vy9dWrxRPSdg==[/tex][/color][color=#000000]，[/color][color=#000000]把厚度为 [/color][tex=4.357x1.429]gYZHjoIO1BlZPKdFpX28hMMWptSg7QAvOpM2aqEceDWcK6lTc/wneE8U/KYACINj[/tex][color=#000000][/color][color=#000000]的金属平板平行于极板插入电容器内[/color][color=#000000]（[/color][color=#000000]不与极板接触[/color][color=#000000]） ．[/color][color=#000000][color=#000000]（１）[/color][color=#000000]计算插入后电容器的电容 [/color][color=#000000]； [/color][color=#000000]（２）[/color][color=#000000]给电容器充电到电势差为[/color][tex=1.071x1.214]FUYNpJbCISw4d+CApcAiKQ==[/tex][color=#000000][/color][color=#000000]后 [/color][color=#000000]，[/color][color=#000000]断开电源 [/color][color=#000000]，[/color][color=#000000]再把金属板从电容器中抽出 [/color][color=#000000]， [/color][color=#000000]外界要作多少功 [/color][color=#000000]？[/color][/color][color=#000000][/color]

    • 1

      [color=#000000]一桶内盛水 [/color][color=#000000]，[/color][color=#000000]系于[/color][color=#000000]绳[/color][color=#000000]的[/color][color=#000000]一[/color][color=#000000]端 [/color][color=#000000]，[/color][color=#000000]并绕 [/color][color=#000000][tex=0.5x0.786]SQhXiI0F7ygwU/RA5gtDkA==[/tex][/color][color=#000000]点以角速度 [/color][color=#000000][tex=0.643x0.786]AXX81H1aJipmZ3Hxs77Mpw==[/tex] [/color][color=#000000]在铅直平面内旋转 [/color][color=#000000]．[/color][color=#000000]设水的质量为[/color][tex=0.929x0.786]D9maNLyVVGrC3QbL9jjRWg==[/tex][color=#000000] [/color][color=#000000]，[/color][color=#000000]桶的质量为 [/color][color=#000000][tex=1.0x1.0]/4LSvKfNeQWJ+IvWbbbjdA==[/tex][/color][color=#000000]，[/color][color=#000000]圆周半径为[/color][tex=0.786x1.0]as0RCzgUx1oS48cKHRAVVg==[/tex][color=#000000] [/color][color=#000000]，[/color][color=#000000]问[/color][tex=0.643x0.786]AXX81H1aJipmZ3Hxs77Mpw==[/tex][color=#000000][/color][color=#000000]为多大[/color][color=#000000]时 [/color][color=#000000]，[/color][color=#000000]才能保证水流不出来 [/color][color=#000000]？[/color]

    • 2

      [color=#000000]一给定的弹簧在 [/color][color=#000000][/color][tex=1.857x1.0]DtSZzJg9UaqZHKutxOamfw==[/tex][color=#000000] [/color][color=#000000]的拉力下伸长了 [/color][color=#000000][/color][tex=2.357x1.0]lmqqIgvXeAN1gAnOq3mfZQ==[/tex][color=#000000][/color][color=#000000]，[/color][color=#000000]质量为[/color][tex=1.5x1.214]Dqu8Me1wUM0HlVj53xPrgw==[/tex][color=#000000][/color][color=#000000]的物体悬在 [/color][color=#000000]弹簧下端并使之静止 [/color][color=#000000]，[/color][color=#000000]再把物体向下拉 [/color][color=#000000][/color][tex=2.357x1.0]Iw7QUiIDjMOCV2bVwcRpTQ==[/tex][color=#000000][/color][color=#000000]，[/color][color=#000000]然[/color][color=#000000]后[/color][color=#000000]释[/color][color=#000000]放 [/color][color=#000000]，[/color][color=#000000]问 [/color][color=#000000]：[/color][color=#000000]物体从平衡位置运动到上面 [/color][color=#000000][/color][tex=1.857x1.0]eD0ltVJ+hZBMdhlv8gCj0w==[/tex][color=#000000][/color][color=#000000]处所需最短的时间是[/color][color=#000000]多少 [/color][color=#000000]？[/color]

    • 3

      [color=#000000]宇宙飞船关闭发动机返回地球的过程 [/color][color=#000000]，[/color][color=#000000]可以认为是仅在地球万有引力作用 [/color][color=#000000]下运动 [/color][color=#000000]．[/color][color=#000000]若用[/color][tex=0.929x0.786]D9maNLyVVGrC3QbL9jjRWg==[/tex][color=#000000][/color][color=#000000]表示飞船质量 [/color][color=#000000]，[/color][color=#000000][tex=1.0x1.0]/4LSvKfNeQWJ+IvWbbbjdA==[/tex] [/color][color=#000000]表示地球质量 [/color][color=#000000]，[/color][color=#000000][tex=0.786x1.0]JTRtgqQ00R3dUQzwS4iwbg==[/tex][/color][color=#000000]表示引力常量 [/color][color=#000000]，[/color][color=#000000]则飞船从距地[/color][color=#000000]球中心[/color][tex=0.857x1.0]BNzznGkXRFuGyw2vMy6rWw==[/tex][color=#000000][/color][color=#000000]处下降到 [/color][color=#000000][/color][tex=0.857x1.0]Fz01PbYkU0SRGm3tB5KjiA==[/tex][color=#000000][/color][color=#000000]处的过程中 [/color][color=#000000]，[/color][color=#000000]动能的增量为[/color][color=#000000]（[/color][color=#000000]    [/color][color=#000000]） ．[/color] 未知类型：{'options': ['[tex=2.929x2.571]ut3pmzdQFRV46C9S+rFMOreWPXNjhLiYDlzYDqj4KjQ=[/tex]', '[tex=2.929x2.714]ut3pmzdQFRV46C9S+rFMOiraPy6DjGfp7iTVyRvWxSc=[/tex]', '[tex=5.429x2.429]fQZIzhK7BVc2I1koSPAIVGUvO07S8z3o8BxipBdCL1yAO9u+ggfAaY8t7WHkHkpP[/tex]', '[tex=5.429x2.571]fQZIzhK7BVc2I1koSPAIVPD3GlEb36u6FVWppCdblhYF36Mr1hGDRtLLsqhZgtHm[/tex]'], 'type': 102}

    • 4

      [color=#000000]一质点作谐振[/color][color=#000000]动 [/color][color=#000000]，[/color][color=#000000]频[/color][color=#000000]率为[/color][tex=0.5x0.786]Ov81hmuvmfMhngaKtMBcFQ==[/tex][color=#000000]，[/color][color=#000000]则[/color][color=#000000]其[/color][color=#000000]振[/color][color=#000000]动动能变[/color][color=#000000]化[/color][color=#000000]频[/color][color=#000000]率[/color][color=#000000]为[/color][color=#000000]（[/color][color=#000000]      [/color][color=#000000]）[/color] 未知类型：{'options': ['[tex=1.429x2.357]w/uX29w8QiV7wl7CApOqBepRKvCnwL0gPxiuiHWV69s=[/tex]', '[tex=1.429x2.357]Sj8Y4rwDiLPs1yv/BxJfglqdn1NDjvzXsyOYtffjU8Y=[/tex]', '[tex=0.5x0.786]dCrI67AYQK6jFSlsbBXzAg==[/tex]', '[tex=1.0x1.0]VNhhwWpOCbOxgVOS+hUMPQ==[/tex]', '[tex=1.0x1.0]d+RdgJ6f1xzS6Hn406qz3g==[/tex]'], 'type': 102}