mid-term-sol

z 2 2 ha x l ha y l z2 h a x

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Unformatted text preview: !!!!!!!!!!!!!!!!!!!!!!!!!!! + j ! 2 2 2 2 2 2 2 2 2 k H− a + x L + H− a + y L + z Ha + x L + H− a + y L + z y 1 z z è!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! z 2 2 Ha + x L + Ha + y L + z2 { H− a + x L + Ha + y L + z In[2]:= efield = 8D@v, xD, D@v, yD, D@v, zD< i j Out[2]= 9kq j− j −a + x 2 k HH − a + x L + H − a + y L + z 2 L 2 a+x L + HH a + x L 2 + H − a + y L 2 + z 2 L + HH a + x L + H − a + y L + 2 2 z2 3 ê2 + 3 ê2 −a + x 3 ê2 i j kq j− j k HH − a + x L + H − a + y L + 2 z2 z HH a + x L + H a + y L + 2 2 z2 L 3 ê2 L HH a + x L 2 + H a + y L 2 + z 2 L 3 ê2 y z, z z { L HH a + x L + H a + y L + HH− a + x L2 + Ha + yL2 + z2 L 3 ê2 − HH− a + x L + Ha + yL + z2 a+y z 2 y z, z z { − 2 i −a + y j + kq j− j 3 ê2 HH − a + x L 2 + H − a + y L 2 + z 2 L k −a + y L 3 ê2 a+x 3 ê2 2 3 ê2 y z= z z { In[3]:= firstterm = D@efield, aD secondterm = D@D@efield, aD, aD + z HH a + x L + H − a + y L + 2 2 z2 L 3 ê2 2 2 z2 a+y + z HH− a + x L + Ha + yL2 + z2 L 2 3 ê2 − phz3113midterm.nb 2 i 3 H− a + x L H− 2 H− a + x L − 2 H− a + y LL j Out[3]= 9kq j + j 5 ê2 k 2 HH− a + x L2 + H− a + y L2 + z 2 L 1 HH − a + x L + H − a + y L + 2 2 L L 3 Ha + xL H2 Ha + x L + 2 Ha + y LL L + 1 HH − a + x L + H a + y L + z2 + + 3 ê2 2 3 Ha + x L H2 Ha + x L − 2 H− a + y LL − 1 3 ê2 HH a + x L 2 + H − a + y L 2 + z 2 L 2 − 2 HHa + xL2 + H− a + yL2 + z2 L 3 H− a + x L H− 2 H− a + x L + 2 Ha + y LL z2 3 ê2 5 ê2 2 HH− a + x L2 + Ha + yL2 + z2 L 2 HHa + x L + Ha + y L + 2 2 z2 L 5 ê2 5 ê2 − z2 L y z, z z { z2 L y z, z z { 1 − HHa + xL + Ha...
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This note was uploaded on 06/01/2013 for the course PHZ 3113 taught by Professor Wang during the Summer '13 term at FIU.

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