3j - Ana-vu— 124 TABLES Table 1 Harmonic Polynomials and...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Ana-vu— 124 TABLES Table 1. Harmonic Polynomials and Spherical Harmonica. (Una-(r) = fl Yin-(a) ‘0) I! m (Blair) YIMCG) W) 1 1 D 0 2%} 2 1r 1 § 1‘]? 1 0 2J;:: 2 1r cos B , 1 :bl :Fl IE. (x :i: iy‘) =‘Fl $7311]. 96‘”, 2 0 iJ—(Zzaxz- ——y) 41J§(:c:sB-smfi) 2 :I:1 =F-‘/1—5 2(1: =I: iy) $ jag-Hf cos 65in 69" ' 2 2w l 1—5 - 2 - 2 ‘Zi' , 23:2 4 2w(m:l:cy) 4142:8111 Be 3 0 :Fgljz (2r;2 — 3:52 — 3y2)z iJZ: (2 cos3 0 — 3 cos Gain2 9) 3 2 2 a . 1 21 2 Q , a —.-. ' -2-1—-(4z — y)(a: :1: 1y) =F§ : (4 cos (ism 0 *- sm 6);: 115-211: 3 :I:2 ; 120w 52(2: :I: W)1 cos 63in2 Be $11:13 taio 3 :l:3 $8 $20 :5: iy) =F- fl} 0e Irreducible tensors containing in addition the components of some other vector 1" may be constructed by polarization of the harmonics with the operator r = r _a_ r __a__ I i '. rV‘xax'l'yay+zaz 1 Cf. Rose (1954). .' r. I E ’ 1 .1- .1.” Table 2. 125 TA BLES .5: + 55 + 5% EN Hunclv : .5 5 w 55ch + 5%“ + 55V g :IV 5.: + 55 + 555 I 3 .3 flEV .TV .55 +55 I 3: + 55 + 3 E.-. c .5 .H+5V : + 5%“ + 58 + 53 .flgqgiifilV m .5 ...~+5V H: + 533 + 5372;2IV «+315 “.5 + ".5 + _.51 5. 323 36 mm 5. a E+a+a+5 .sz . V .w “53:.“ HahH V A”..- “T35! H5. A. coo .V on? .5 .5 H+5. H+H Hm ..V ..V ...V ..V ...V .55 mm 5. m ooc "555.5 w a + EVAN + 3V8 + RVG + 33 + RV cIV a+EI38+:I32+E+ba+3+§ a; . , a + Ea + 3V5 + ~qu + 3V3 + 2V I V H :I E V a V. «+5 V *7: I a: + s I 3 + 2 I as + s + L32 Va A“ V. Ni. fl 3 + EVAN + EVA” + EV? + 3V3 + RV H :IV Au NIEI E v a + 3 I 32 + E I 33 I a: I E I 3 a; m V. “+5 5 a a: + 3V8 + EVE + RV I w MIST E .,,..a m v AHITNémITHVm—H «ITEMIH. H_T 2T 5: Am 5 «+5 A . 56+H ml I I a T fl 3: + EVAN + 3V8 + 3V T QI V m n 2 a h Am + E + 2m + E I 3m. I E I an m V. «+5 fl 2 + EVAN + EVE + RV? + EV :I V w «IEI E AW+E+E$+EI3$+EI§ E: m a T1, ma}; a “I I I _m 2 + 3V3 + EVE + RV? + HM~53 :IV m m E 3 m + E I 3% + E I meI I LET H w a mi 83353 a as: 6 2 1... @413 TA BLES a .5 his * fl H E + E. I “3% a I 356: + Ea + $5 + B * SIBQ+E+§ : I 358: + Ea + 5% + 3 am: + Rx“ + as + E? + 3 a 2+EI32+E+3¢ R: + 2.5 + as + 35 + 3 H SN 3: + Ea + as + 35 + as a + E + 3: + E I 33 I 3: I E I aLETEIVm . a... EQSHAnrrfing . . 3 I 358: + Rx“ + 38 + a: #93 + 939$ a + E + 3: + E + 2: I b: I E I 3L=LTV I b: + E I 3 gen + Em + 39:32; 31;. .uiwzfiqqixfiwiw, 32¢ Am a a Taiici ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern