{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Background image of page 6
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]:=
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}