求教大学物理量子力学的一道轨道角动量题目 书上的公式里面根本没有这个l啊?要怎么做呢? 餐卡o答案 求大学物理上册所有重要公式、满意可加分!!

\u4e00\u9053\u91cf\u5b50\u529b\u5b66\u9898

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\u0394p\u00b7\u0394x~h
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\u0394L_z=\u0394p*r
\u89d2\u5ea6\u7684\u8bef\u5dee\u4e3a
\u0394\u03c8=\u0394x/r
\u8fd9\u91cc\u0394x\u662f\u5f27\u957f\u7684\u8bef\u5dee\u3002\u4e24\u8005\u76f8\u4e58\uff0c\u5f97\u5230
\u0394L_z\u00b7\u0394\u03c8=\u0394p\u00b7\u0394x~h

\u8fd9\u9053\u9898\u592a\u81ed\u4e86\u3002\u9996\u5148\u5b83\u9664\u4e86\u7528\u4e86\u6d4b\u4e0d\u51c6\u516c\u5f0f\u4e4b\u5916\uff0c\u6ca1\u7528\u5230\u4efb\u4f55\u91cf\u5b50\u529b\u5b66\u7684\u77e5\u8bc6\u3002\u66f4\u7cdf\u7cd5\u7684\uff0c\u5b83\u4f1a\u8bef\u5bfc\u5b66\u751f\u3002\u771f\u6b63\u5173\u4e8e\u89d2\u52a8\u91cf\u7684\u6d4b\u4e0d\u51c6\u5173\u7cfb\u4e0d\u662f\u8fd9\u6837\u7684\uff0c\u800c\u662f
[L_x,L_y]=ihL_z
\u51fa\u8fd9\u79cd\u9898\u7684\u8001\u5e08\u4e0d\u5e94\u8be5\u6559\u91cf\u5b50\u529b\u5b66\u3002

\u6982\u5ff5\uff08\u5b9a\u4e49\u548c\u76f8\u5173\u516c\u5f0f\uff09
1\uff0e \u4f4d\u7f6e\u77e2\u91cf\uff1a \uff0c\u5176\u5728\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\uff1a \uff1b \u89d2\u4f4d\u7f6e\uff1a\u03b8
2\uff0e \u901f\u5ea6\uff1a \u5e73\u5747\u901f\u5ea6\uff1a \u901f\u7387\uff1a \uff08 \uff09\u89d2\u901f\u5ea6\uff1a
\u89d2\u901f\u5ea6\u4e0e\u901f\u5ea6\u7684\u5173\u7cfb\uff1aV=r\u03c9
3\uff0e \u52a0\u901f\u5ea6\uff1a \u6216 \u5e73\u5747\u52a0\u901f\u5ea6\uff1a \u89d2\u52a0\u901f\u5ea6\uff1a
\u5728\u81ea\u7136\u5750\u6807\u7cfb\u4e2d \u5176\u4e2d \uff08=r\u03b2\uff09\uff0c \uff08=r2 \u03c9\uff09
4\uff0e \u529b\uff1a =m \uff08\u6216 = \uff09 \u529b\u77e9\uff1a \uff08\u5927\u5c0f\uff1aM=rFcos\u03b8\u65b9\u5411\uff1a\u53f3\u624b\u87ba\u65cb\u6cd5\u5219\uff09
5\uff0e \u52a8\u91cf\uff1a \uff0c\u89d2\u52a8\u91cf\uff1a \uff08\u5927\u5c0f\uff1aL=rmvcos\u03b8\u65b9\u5411\uff1a\u53f3\u624b\u87ba\u65cb\u6cd5\u5219\uff09
6\uff0e \u51b2\u91cf\uff1a \uff08= \u0394t\uff09\uff1b\u529f\uff1a \uff08\u6c14\u4f53\u5bf9\u5916\u505a\u529f\uff1aA=\u222bPdV\uff09
mg(\u91cd\u529b) \u2192 mgh
-kx\uff08\u5f39\u6027\u529b\uff09 \u2192 kx2/2
F= (\u4e07\u6709\u5f15\u529b) \u2192 =Ep
(\u9759\u7535\u529b) \u2192
7\uff0e \u52a8\u80fd\uff1amV2/2
8\uff0e \u52bf\u80fd\uff1aA\u4fdd= \u2013 \u0394Ep\u4e0d\u540c\u76f8\u4e92\u4f5c\u7528\u529b\u52bf\u80fd\u5f62\u5f0f\u4e0d\u540c\u4e14\u96f6\u70b9\u9009\u62e9\u4e0d\u540c\u5176\u5f62\u5f0f\u4e0d\u540c\uff0c\u5728\u9ed8\u8ba4\u52bf\u80fd\u96f6\u70b9\u7684\u60c5\u51b5\u4e0b\uff1a
\u673a\u68b0\u80fd\uff1aE=EK+EP
9\uff0e \u70ed\u91cf\uff1a \u5176\u4e2d\uff1a\u6469\u5c14\u70ed\u5bb9\u91cfC\u4e0e\u8fc7\u7a0b\u6709\u5173\uff0c\u7b49\u5bb9\u70ed\u5bb9\u91cfCv\u4e0e\u7b49\u538b\u70ed\u5bb9\u91cfCp\u4e4b\u95f4\u7684\u5173\u7cfb\u4e3a\uff1aCp= Cv+R
10\uff0e \u538b\u5f3a\uff1a
11\uff0e \u5206\u5b50\u5e73\u5747\u5e73\u52a8\u80fd\uff1a \uff1b\u7406\u60f3\u6c14\u4f53\u5185\u80fd\uff1a
12\uff0e \u9ea6\u514b\u65af\u97e6\u901f\u7387\u5206\u5e03\u51fd\u6570\uff1a \uff08\u610f\u4e49\uff1a\u5728V\u9644\u8fd1\u5355\u4f4d\u901f\u5ea6\u95f4\u9694\u5185\u7684\u5206\u5b50\u6570\u6240\u5360\u6bd4\u7387\uff09
13\uff0e \u5e73\u5747\u901f\u7387\uff1a
\u65b9\u5747\u6839\u901f\u7387\uff1a \uff1b\u6700\u53ef\u51e0\u901f\u7387\uff1a
14\uff0e \u71b5\uff1aS=Kln\u03a9\uff08\u03a9\u4e3a\u70ed\u529b\u5b66\u51e0\u7387\uff0c\u5373\uff1a\u4e00\u79cd\u5b8f\u89c2\u6001\u5305\u542b\u7684\u5fae\u89c2\u6001\u6570\uff09
15\uff0e \u7535\u573a\u5f3a\u5ea6\uff1a = /q0 \uff08\u5bf9\u70b9\u7535\u8377\uff1a \uff09
16\uff0e \u7535\u52bf\uff1a \uff08\u5bf9\u70b9\u7535\u8377 \uff09\uff1b\u7535\u52bf\u80fd\uff1aWa=qUa(A= \u2013\u0394W)
17\uff0e \u7535\u5bb9\uff1aC=Q/U \uff1b\u7535\u5bb9\u5668\u50a8\u80fd\uff1aW=CU2/2\uff1b\u7535\u573a\u80fd\u91cf\u5bc6\u5ea6\u03c9e=\u03b50E2/2
18\uff0e \u78c1\u611f\u5e94\u5f3a\u5ea6\uff1a\u5927\u5c0f\uff0cB=Fmax/qv(T)\uff1b\u65b9\u5411\uff0c\u5c0f\u78c1\u9488\u6307\u5411\uff08S\u2192N\uff09\u3002
\u5b9a\u5f8b\u548c\u5b9a\u7406
1\uff0e \u77e2\u91cf\u53e0\u52a0\u539f\u7406\uff1a\u4efb\u610f\u4e00\u77e2\u91cf \u53ef\u770b\u6210\u5176\u72ec\u7acb\u7684\u5206\u91cf \u7684\u548c\u3002\u5373\uff1a =\u2211 \uff08\u628a\u5f0f\u4e2d \u6362\u6210 \u3001 \u3001 \u3001 \u3001 \u3001 \u5c31\u5206\u522b\u6210\u4e86\u4f4d\u7f6e\u3001\u901f\u5ea6\u3001\u52a0\u901f\u5ea6\u3001\u529b\u3001\u7535\u573a\u5f3a\u5ea6\u548c\u78c1\u611f\u5e94\u5f3a\u5ea6\u7684\u53e0\u52a0\u539f\u7406\uff09\u3002
2\uff0e \u725b\u987f\u5b9a\u5f8b\uff1a =m \uff08\u6216 = \uff09\uff1b\u725b\u987f\u7b2c\u4e09\u5b9a\u5f8b\uff1a \u2032= \uff1b\u4e07\u6709\u5f15\u529b\u5b9a\u5f8b\uff1a
3\uff0e \u52a8\u91cf\u5b9a\u7406\uff1a \u2192\u52a8\u91cf\u5b88\u6052\uff1a \u6761\u4ef6
4\uff0e \u89d2\u52a8\u91cf\u5b9a\u7406\uff1a \u2192\u89d2\u52a8\u91cf\u5b88\u6052\uff1a \u6761\u4ef6
5\uff0e \u52a8\u80fd\u539f\u7406\uff1a \uff08\u6bd4\u8f83\u52bf\u80fd\u5b9a\u4e49\u5f0f\uff1a \uff09
6\uff0e \u529f\u80fd\u539f\u7406\uff1aA\u5916+A\u975e\u4fdd\u5185=\u0394E\u2192\u673a\u68b0\u80fd\u5b88\u6052\uff1a\u0394E=0\u6761\u4ef6A\u5916+A\u975e\u4fdd\u5185=0
7\uff0e \u7406\u60f3\u6c14\u4f53\u72b6\u6001\u65b9\u7a0b\uff1a \u6216P=nkT\uff08n=N/V\uff0ck=R/N0\uff09
8\uff0e \u80fd\u91cf\u5747\u5206\u539f\u7406\uff1a\u5728\u5e73\u8861\u6001\u4e0b\uff0c\u7269\u8d28\u5206\u5b50\u7684\u6bcf\u4e2a\u81ea\u7531\u5ea6\u90fd\u5177\u6709\u76f8\u540c\u7684\u5e73\u5747\u52a8\u80fd\uff0c\u5176\u5927\u5c0f\u90fd\u4e3akT/2\u3002
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\u5b9e\u8d28\uff1a\u5728\u5b64\u7acb\u7cfb\u7edf\u5185\u90e8\u53d1\u751f\u7684\u8fc7\u7a0b\uff0c\u603b\u662f\u7531\u70ed\u529b\u5b66\u6982\u7387\u5c0f\u7684\u5b8f\u89c2\u72b6\u6001\u5411\u70ed\u529b\u5b66\u6982\u7387\u5927\u7684\u72b6\u6001\u8fdb\u884c\u3002\u4ea6\u5373\u5728\u5b64\u7acb\u7cfb\u7edf\u5185\u90e8\u6240\u53d1\u751f\u7684\u8fc7\u7a0b\u603b\u662f\u6cbf\u7740\u65e0\u5e8f\u6027\u589e\u5927\u7684\u65b9\u5411\u8fdb\u884c\u3002
9\uff0e \u70ed\u529b\u5b66\u7b2c\u4e00\u5b9a\u5f8b\uff1a\u0394E=Q+A
10\uff0e\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\uff1a \u5b64\u7acb\u7cfb\u7edf\uff1a\u0394S>0
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11\uff0e \u5e93\u4ed1\u5b9a\u5f8b\uff1a
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12\uff0e \u9ad8\u65af\u5b9a\u7406\uff1a \uff08\u9759\u7535\u573a\u662f\u6709\u6e90\u573a\uff09\u2192\u65e0\u7a77\u5927\u5e73\u677f\uff1aE=\u03c3/2\u03b50
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= /q0 \u5355\u4f4d\uff1aN/C =V/m
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=q( + \u00d7 )\u6d1b\u4ed1\u5179\u516c\u5f0f
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-q +q
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\u2463\u7535\u5076\u6781\u77e9\uff1a =q \u78c1\u77e9\uff1a =I =IS
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*\u81ea\u611f\uff1aL=\u03a8/I \u5355\u4f4d\uff1a\u4ea8\u5229\uff08H\uff09
*\u4e92\u611f\uff1aM=\u03a821/I1=\u03a812/I2 \u5355\u4f4d\uff1a\u4ea8\u5229\uff08H\uff09

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\u2466*\u80fd\u6d41\u5bc6\u5ea6\uff1a

2\uff0e \u5b9e\u9a8c\u5b9a\u5f8b
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\u611f\u751f\u7535\u52a8\u52bf\uff1a \uff08 i\u4e3a\u611f\u751f\u7535\u573a\uff09
*\u2464\u6b27\u59c6\u5b9a\u5f8b\uff1aU=IR\uff08 =\u03c1 \uff09\u5176\u4e2d\u03c1\u4e3a\u7535\u5bfc\u7387
3\uff0e *\u5b9a\u7406\uff08\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7ec4\uff09
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4\uff0e \u5e38\u7528\u516c\u5f0f
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\u2461 \u5e26\u7535\u7c92\u5b50\u5728\u5300\u5f3a\u78c1\u573a\u4e2d\uff1a\u534a\u5f84 \u5468\u671f
\u78c1\u77e9\u5728\u5300\u5f3a\u78c1\u573a\u4e2d\uff1a\u53d7\u529bF=0\uff1b\u53d7\u529b\u77e9
\u2462\u7535\u5bb9\u5668\u50a8\u80fd\uff1aWc= CU2 *\u7535\u573a\u80fd\u91cf\u5bc6\u5ea6\uff1a\u03c9e= \u03b50E2 \u7535\u78c1\u573a\u80fd\u91cf\u5bc6\u5ea6\uff1a\u03c9= \u03b50E2+ B2
*\u7535\u611f\u50a8\u80fd\uff1aWL= LI2 *\u78c1\u573a\u80fd\u91cf\u5bc6\u5ea6\uff1a\u03c9B= B2 \u7535\u78c1\u573a\u80fd\u6d41\u5bc6\u5ea6\uff1aS=\u03c9V
\u2463 *\u7535\u78c1\u6ce2\uff1aC= =3.0\u00d7108m/s \u5728\u4ecb\u8d28\u4e2dV=C/n\uff0c\u9891\u7387f=\u03bd=
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1\uff0e \u5b9a\u4e49\u548c\u6982\u5ff5
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\u03be=Acos(\u03c9t+\u03c6-2\u03c0x/\u03bb) \u7b80\u8c10\u632f\u52a8\u65b9\u7a0b\uff1a\u03be=Acos(\u03c9t+\u03c6)
\u6ce2\u5f62\u65b9\u7a0b\uff1a\u03be=Acos(2\u03c0x/\u03bb+\u03c6\u2032)

\u76f8\u4f4d\u03a6\u2014\u2014\u51b3\u5b9a\u632f\u52a8\u72b6\u6001\u7684\u91cf
\u632f\u5e45A\u2014\u2014\u632f\u52a8\u91cf\u6700\u5927\u503c \u51b3\u5b9a\u4e8e\u521d\u6001 x0=Acos\u03c6
\u521d\u76f8\u03c6\u2014\u2014x=0\u5904t=0\u65f6\u76f8\u4f4d \uff08x0,V0\uff09 V0= \u2013A\u03c9sin\u03c6
\u9891\u7387\u03bd\u2014\u2014\u6bcf\u79d2\u632f\u52a8\u7684\u6b21\u6570
\u5706\u9891\u7387\u03c9=2\u03c0\u03bd \u51b3\u5b9a\u4e8e\u6ce2\u6e90\u5982\uff1a \u5f39\u7c27\u632f\u5b50\u03c9=
\u5468\u671fT\u2014\u2014\u632f\u52a8\u4e00\u6b21\u7684\u65f6\u95f4 \u5355\u6446\u03c9=
\u6ce2\u901fV\u2014\u2014\u6ce2\u7684\u76f8\u4f4d\u4f20\u64ad\u901f\u5ea6\u6216\u80fd\u91cf\u4f20\u64ad\u901f\u5ea6\u3002\u51b3\u5b9a\u4e8e\u4ecb\u8d28\u5982\uff1a \u7ef3V= \u5149\u901fV=C/n
\u7a7a\u6c14V=
\u6ce2\u7684\u5e72\u6d89\uff1a\u540c\u632f\u52a8\u65b9\u5411\u3001\u540c\u9891\u7387\u3001\u76f8\u4f4d\u5dee\u6052\u5b9a\u7684\u6ce2\u7684\u53e0\u52a0\u3002
\u5149\u7a0b\uff1aL=nx\uff08\u5373\u5149\u8d70\u8fc7\u7684\u51e0\u4f55\u8def\u7a0b\u4e0e\u4ecb\u8d28\u7684\u6298\u5c04\u7387\u7684\u4e58\u79ef\u3002
\u76f8\u4f4d\u7a81\u53d8\uff1a\u6ce2\u4ece\u6ce2\u758f\u5a92\u8d28\u8fdb\u5165\u6ce2\u5bc6\u5a92\u8d28\u65f6\u6709\u76f8\u4f4d\u03c0\u7684\u7a81\u53d8\uff08\u6298\u5408\u5149\u7a0b\u4e3a\u03bb/2\uff09\u3002
\u62cd\uff1a\u9891\u7387\u76f8\u8fd1\u7684\u4e24\u4e2a\u632f\u52a8\u7684\u5408\u6210\u632f\u52a8\u3002
\u9a7b\u6ce2\uff1a\u4e24\u5217\u5b8c\u5168\u76f8\u540c\u4ec5\u65b9\u5411\u76f8\u53cd\u7684\u6ce2\u7684\u5408\u6210\u6ce2\u3002
\u591a\u666e\u52d2\u6548\u5e94\uff1a\u56e0\u6ce2\u6e90\u4e0e\u89c2\u5bdf\u8005\u76f8\u5bf9\u8fd0\u52a8\u4ea7\u751f\u7684\u9891\u7387\u6539\u53d8\u7684\u73b0\u8c61\u3002
\u884d\u5c04\uff1a\u5149\u504f\u79bb\u76f4\u7ebf\u4f20\u64ad\u7684\u73b0\u8c61\u3002
\u81ea\u7136\u5149\uff1a\u4e00\u822c\u5149\u6e90\u53d1\u51fa\u7684\u5149
\u504f\u632f\u5149\uff08\u4ea6\u79f0\u7ebf\u504f\u632f\u5149\u6216\u79f0\u5e73\u9762\u504f\u632f\u5149\uff09\uff1a\u53ea\u6709\u4e00\u4e2a\u65b9\u5411\u632f\u52a8\u6210\u4efd\u7684\u5149\u3002
\u90e8\u5206\u504f\u632f\u5149\uff1a\u5404\u632f\u52a8\u65b9\u5411\u6982\u7387\u4e0d\u7b49\u7684\u5149\u3002\u53ef\u770b\u6210\u76f8\u4e92\u5782\u76f4\u4e24\u632f\u5e45\u4e0d\u540c\u7684\u5149\u7684\u5408\u6210\u3002
2\uff0e \u65b9\u6cd5\u3001\u5b9a\u5f8b\u548c\u5b9a\u7406

\u03c9 \u03c6
o x

\u2460 \u65cb\u8f6c\u77e2\u91cf\u6cd5\uff1a
A
A1 A2
o x
\u5982\u56fe\uff0c\u4efb\u610f\u4e00\u4e2a\u7b80\u8c10\u632f\u52a8\u03be=Acos(\u03c9t+\u03c6)\u53ef\u770b\u6210\u521d\u59cb\u89d2\u4f4d\u7f6e\u4e3a\u03c6\u4ee5\u03c9\u9006\u65f6\u9488\u65cb\u8f6c\u7684\u77e2\u91cf \u5728x\u65b9\u5411\u7684\u6295\u5f71\u3002
\u76f8\u5e72\u5149\u5408\u6210\u632f\u5e45\uff1a
A=

\u5176\u4e2d\uff1a\u0394\u03c6=\u03c61-\u03c62\u2013 \uff08r2\u2013r1\uff09\u5f53\u0394\u03c6=
\u5f53\u03c61-\u03c62=0\u65f6\uff0c\u5149\u7a0b\u5dee\u03b4=\uff08r2\u2013r1\uff09=

\u2461 \u60e0\u66f4\u65af\u539f\u7406\uff1a\u6ce2\u9762\u5b50\u6ce2\u7684\u5305\u7edc\u9762\u4e3a\u65b0\u6ce2\u524d\u3002\uff08\u7528\u6765\u5224\u65ad\u6ce2\u7684\u4f20\u64ad\u65b9\u5411\uff09
I1 \u03b8 I2 \u9a6c\u5415\u65af\u5b9a\u5f8b
\u2462 \u83f2\u6d85\u5c14\u539f\u7406\uff1a\u6ce2\u9762\u5b50\u6ce2\u76f8\u5e72\u53e0\u52a0\u786e\u5b9a\u5176\u540e\u4efb\u4e00\u70b9\u7684\u632f\u52a8\u3002
\u2463 *\u9a6c\u5415\u65af\u5b9a\u5f8b\uff1aI2=I1cos2\u03b8
\u2464 *\u5e03\u5112\u65af\u7279\u5b9a\u5f8b\uff1a
iP

n1 Ip+\u03b3=90\u00b0
n2
\u03b3 \u5e03\u5112\u65af\u7279\u5b9a\u5f8b
\u5f53\u5165\u5c04\u5149\u4ee5Ip\u5165\u5c04\u89d2\u5165\u5c04\u65f6\u5219\u53cd\u5c04\u5149\u4e3a\u5782\u76f4\u5165\u5c04\u9762\u632f\u52a8\u7684\u5b8c\u5168\u504f\u632f\u5149\u3002Ip\u79f0\u5e03\u5112\u65af\u7279\u89d2\uff0c\u5176\u6ee1\u8db3\uff1a
tg ip = n2/n1

3\uff0e \u516c\u5f0f
\u632f\u52a8\u80fd\u91cf\uff1aEk=mV2/2=Ek(t) E= Ek +Ep=kA2/2
Ep=kx2/2= (t)
*\u6ce2\u52a8\u80fd\u91cf\uff1a I= \u221dA2

*\u9a7b\u6ce2\uff1a
\u2190 \u03bb \u2192

L
\u6ce2\u8282\u95f4\u8dddd=\u03bb/2
\u57fa\u6ce2\u6ce2\u957f\u03bb0=2L
\u57fa\u9891\uff1a\u03bd0=V/\u03bb0=V/2L\uff1b
\u8c10\u9891\uff1a\u03bd=n\u03bd0
*\u591a\u666e\u52d2\u6548\u5e94\uff1a
\u673a\u68b0\u6ce2 \uff08VR\u2014\u2014\u89c2\u5bdf\u8005\u901f\u5ea6\uff1bVs\u2014\u2014\u6ce2\u6e90\u901f\u5ea6\uff09
\u5bf9\u5149\u6ce2 \u5176\u4e2dVr\u6307\u5149\u6e90\u4e0e\u89c2\u5bdf\u8005\u76f8\u5bf9\u901f\u5ea6\u3002
y
\u0394y
d \u03b8

\u6768\u6c0f\u53cc\u7f1d\uff1a dsin\u03b8=k\u03bb\uff08\u660e\u7eb9\uff09
\u03b8\u2248sin\u03b8\u2248y/D
\u6761\u7eb9\u95f4\u8ddd\u0394y=D/\u03bbd

y

a \u03b8
f

\u5355\u7f1d\u884d\u5c04\uff08\u592b\u7405\u79be\u8d39\u884d\u5c04\uff09\uff1a
asin\u03b8=k\u03bb\uff08\u6697\u7eb9\uff09
\u03b8\u2248sin\u03b8\u2248y/f

\u745e\u5229\u5224\u636e\uff1a
\u03b8min=1/R =1.22\u03bb/D\uff08\u6700\u5c0f\u5206\u8fa8\u89d2\uff09
y
d
\u03b8
f
\u5149\u6805\uff1a
dsin\u03b8=k\u03bb\uff08\u660e\u7eb9\u5373\u4e3b\u6781\u5927\u6ee1\u8db3\u6761\u4ef6\uff09
tg\u03b8=y/f
d=1/n=L/N\uff08\u5149\u6805\u5e38\u6570\uff09
\u8584\u819c\u5e72\u6d89\uff1a\uff08\u5782\u76f4\u5165\u5c04\uff09
1 2
n1
t n2
n3
\u03b4\u53cd=2n2t+\u03b40 \u03b40= 0 \u4e2d
\u03bb/2 \u6781
\u589e\u53cd\uff1a\u03b4\u53cd=(2k+1)\u03bb/2
\u589e\u900f\uff1a\u03b4\u53cd=k\u03bb

\u73b0\u4ee3\u7269\u7406
\uff08\u4e00\uff09\u91cf\u5b50\u529b\u5b66
1\uff0e \u666e\u6717\u514b\u63d0\u51fa\u80fd\u91cf\u91cf\u5b50\u5316\uff1a\u03b5=h\u03bd\uff08\u6700\u5c0f\u4e00\u4efd\u80fd\u91cf\u503c\uff09
2\uff0e \u7231\u56e0\u65af\u5766\u63d0\u51fa\u5149\u5b50\u5047\u8bf4\uff1a\u5149\u675f\u662f\u5149\u5b50\u6d41\u3002
\u5149\u7535\u6548\u5e94\u65b9\u7a0b\uff1ah\u03bd= mv2+A \u5176\u4e2d\uff1a \u9038\u51fa\u529fA=h\u03bd0\uff08\u03bd0\u7ea2\u9650\u9891\u7387\uff09
\u6700\u5927\u521d\u52a8\u80fd mv2=eUa\uff08Ua\u904f\u6b62\u7535\u538b\uff09
3\uff0e \u5fb7\u5e03\u7f57\u610f\u63d0\u51fa\u7269\u8d28\u6ce2\u7406\u8bba\uff1a\u5b9e\u7269\u7c92\u5b50\u4e5f\u5177\u6709\u6ce2\u52a8\u6027\u3002
\u5219\u5b9e\u7269\u7c92\u5b50\u5177\u6709\u6ce2\u7c92\u4e8c\u8c61\u6027\uff1a\u03b5=h\u03bd=mc2 \u5bf9\u6bd4\u5149\u7684\u4e8c\u8c61\u6027\uff1a \u03b5=h\u03bd=mc2
p=h/\u03bb=mv p=h/\u03bb=mc
\u6ce8\uff1a\u5bf9\u5b9e\u7269\u7c92\u5b50\uff1a >0\u4e14\u03bd\u2260c/\u03bb\u4ea6\u03bd\u2260V/\u03bb\uff1b\u800c\u5bf9\u5149\u5b50\uff1am0=0\u4e14\u03bd=C/\u03bb
4\uff0e\u6d77\u68ee\u4f2f\u4e0d\u786e\u5b9a\u5173\u7cfb\uff1a \u0394x\u0394px\u2265h/4\u03c0 \u0394t\u0394E\u2265h/4\u03c0
\u6ce2\u51fd\u6570\u610f\u4e49\uff1a =\u7c92\u5b50\u5728t\u65f6\u523br\u5904\u51e0\u7387\u5bc6\u5ea6\u3002
\u5f52\u4e00\u5316\u6761\u4ef6\uff1a \u03a8\u7684\u6807\u51c6\u6761\u4ef6\uff1a\u8fde\u7eed\u3001\u6709\u9650\u3001\u5355\u503c\u3002
\uff08\u4e8c\uff09\u72ed\u4e49\u76f8\u5bf9\u8bba\uff1a
1\uff0e\u4e24\u4e2a\u57fa\u672c\u5047\u8bbe\uff1a\u2460\u5149\u901f\u4e0d\u53d8\u539f\u7406\uff1a\u771f\u7a7a\u4e2d\u5728\u6240\u6709\u60ef\u6027\u7cfb\u4e2d\u5149\u901f\u76f8\u540c\uff0c\u4e0e\u5149\u6e90\u8fd0\u52a8\u65e0\u5173\u3002
\u2461\u72ed\u4e49\u76f8\u5bf9\u6027\u539f\u7406\uff1a\u4e00\u5207\u7269\u7406\u5b9a\u5f8b\u5728\u6240\u6709\u60ef\u6027\u7cfb\u4e2d\u90fd\u6210\u7acb\u3002
2\uff0e\u6d1b\u4ed1\u5179\u53d8\u6362\uff1a
\u2211\u2019\u7cfb\u2192\u2211\u7cfb \u2211\u7cfb\u2192\u2211\u2019\u7cfb
x=\u03b3(x\u2019+vt\u2019) x\u2019=\u03b3(x - vt)
y=y\u2019 y\u2019=y
z=z\u2019 z\u2019=z
t=\u03b3(t\u2019+vx\u2019/c2) t\u2019=\u03b3(t-vx/c2)
\u5176\u4e2d\uff1a \u56e0V\u603b\u5c0f\u4e8eC\u5219\u03b3\u22650\u6240\u4ee5\u79f0\u5176\u4e3a\u81a8\u80c0\u56e0\u5b50\uff1b\u79f0\u03b2= \u4e3a\u6536\u7f29\u56e0\u5b50\u3002
3\uff0e\u72ed\u4e49\u76f8\u5bf9\u8bba\u7684\u65f6\u7a7a\u89c2\uff1a
\u2460\u540c\u65f6\u7684\u76f8\u5bf9\u6027\uff1a\u7531\u0394t=\u03b3(\u0394t\u2019+v\u0394x\u2019/c2)\uff0c\u0394t\u2019=0\u65f6\uff0c\u4e00\u822c\u0394t\u22600\u3002\u79f0x\u2019/c2\u4e3a\u540c\u65f6\u6027\u56e0\u5b50\u3002
\u2461\u8fd0\u52a8\u7684\u957f\u5ea6\u7f29\u77ed\uff1a\u0394x=\u0394x\u2019/\u03b3\u2264\u0394x\u2032
\u2462\u8fd0\u52a8\u7684\u949f\u53d8\u6162\uff1a\u0394t=\u03b3\u0394t\u2019\u2265\u0394t\u2032
4\uff0e\u51e0\u4e2a\u91cd\u8981\u7684\u52a8\u529b\u5b66\u5173\u7cfb\uff1a
\u2460 \u8d28\u901f\u5173\u7cfbm=\u03b3m0
\u2461 \u8d28\u80fd\u5173\u7cfbE=mc2 \u7c92\u5b50\u7684\u9759\u6b62\u80fd\u91cf\u4e3a\uff1aE0=m0c2
\u7c92\u5b50\u7684\u52a8\u80fd\u4e3a\uff1aEK=mc2 \u2013 m0c2=
\u5f53V<<c\u65f6\uff0cEK\u2248mV2/2
*\u2462 \u52a8\u91cf\u4e0e\u80fd\u91cf\u5173\u7cfb\uff1aE2\u2013p2c2=E02
*5\uff0e\u901f\u5ea6\u53d8\u6362\u5173\u7cfb\uff1a
\u2211\u2019\u7cfb\u2192\u2211\u7cfb\uff1a
\u2211\u7cfb\u2192\u2211\u2019\u7cfb\uff1a

轨道角动量L^2=l(l+1)h/2pi,磁量子数m=正负l,正负l-1...正负1,0。磁场分量Lz=mh/2pi。将l=2带入,对L^2开方得,L=正负根号下(2乘(2+1))h/2pi=正负根号6h/2pi。
m可取正负2,正负1,0,带入得0,正负h/2pi,正负2h/2pi。也就是答案。

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