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Solutions+7

# Solutions+7 - In[340:= f = [email protected] 2 [email protected] Pi 3D [email protected] PiDL...

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In[340]:= f = Sqrt @H 1 + 2Cos @ qPi ê 3 D Cos @ qPi DL ^2 + H 2Cos @ qPi ê 3 D Sin @ qPi DL ^2 D Out[340]= 1 + 2Cos B p q 3 F Cos @ p q D 2 + 4Cos B p q 3 F 2 Sin @ p q D 2 In[341]:= t = - 3.033 a = 0.129 Out[341]= - 3.033 Out[342]= 0.129 In[343]:= ekplus = tf ê H 1 + af L Out[343]= - 3.033 I 1 + 2Cos A p q 3 E Cos @ p q DM 2 + 4Cos A p q 3 E 2 Sin @ p q D 2 1 + 0.129 I 1 + 2Cos A p q 3 E Cos @ p q DM 2 + 4Cos A p q 3 E 2 Sin @ p q D 2 In[344]:= ekminus = - tf ê H 1 - af L Out[344]= 3.033 I 1 + 2Cos A p q 3 E Cos @ p q DM 2 + 4Cos A p q 3 E 2 Sin @ p q D 2 1 - 0.129 I 1 + 2Cos A p q 3 E Cos @ p q DM 2 + 4Cos A p q 3 E 2 Sin @ p q D 2 In[345]:= Plot @8 ekplus,ekminus < , 8 q,0,1 <D Out[345]= 0.2 0.4 0.6 0.8 1.0 - 5 5 10 15 In[346]:= Series @ ekplus, 8 q,1,2 <D Out[346]= - 11.0025 H q - 1 L + 11.8008 H q - 1 L 2 + O @ q - 1 D 3 In[347]:= Series @ ekminus, 8 q,1,2 <D Out[347]= 11.0025 H q - 1 L - 1.50338 H q - 1 L 2 + O @ q - 1 D 3 In[349]:= a = . In[350]:= fk = Sqrt @H 1 + 2Cos @ kxa ê 2 D Cos @ kyaSqrt @ 3 D ê 2 DL ^2 + H 2Cos @ kxa ê 2 D Sin @ kyaSqrt @ 3 D ê 2 DL ^2 D Out[350]= . 1 + 2Cos B akx 2 F Cos B 1 2 3 aky F 2 + 4Cos B akx 2 F 2 Sin B 1 2 3 aky F 2
In[378]:= fsq = HH fk ê . 8 kx Ø 2Pi ê a ê 3 + dx, ky Ø 2Pi ê a ê Sqrt @ 3 D + dy < L ^2 êê FullSimplify L ê . a Ø 1 Out[378]= 3 - 2Sin B dx + p 6 F - 4Cos B 3 dy 2 F Sin B 1 6 H - 3dx + p LF In[381]:= ExpandAll @ fsq D êê TrigExpand êê Simplify Out[381]= 3 - Cos B dx 2 F 2 - 2Cos B dx 2 F Cos B 3 dy 2 F + 2 3 Cos B 3 dy 2 F Sin B dx 2 F + Sin B dx 2 F 2 - 3 Sin @ dx D In[382]:=

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