Question

(0,31 es un espacio Lumpic . TUTU y Justica. (m 4. (72) Calcular el adjunto del operador S definido de la manera siguiente: S:12 (N) ► 12(N): (ay, az, az ....) - (0, az, az ....)

"S" is an operator that goes from space l^2(N) tomthe same space l^2(N), definides as follows:

(a1,a2,...) to (a2,a3,...). Find the self-adjoint

Answer 1

S: enco) + frem be an operator defined by 5C(4, .-.-.)) = (22, 43, ----) Now To find adjoint of the operators. as, a.....) EY"(N) & (bo, be ---) EX^(N) Now led to loq, Q ----) E Juin ţ1 let s* be the adjoint of s tore lsa, b) = <a,stb) then we have Ha, b6 JUN) Now let a = Com jQj ----) CANON) f b= (bioko ...) € 1" (N.) <sa, b) = ((Q2, ag, ---), (biobeo--)) ] = 2:0 + Žai Ting a scan. a...-), (0, bus bz ---->> 12 Since < 5 (4 09----), (bisbe --)>= (cyga21.--), 5* (b1 by b3 -->> 5604.9.--), CQ, bob2_.--))=((ayyez-), s*(b)-4--)) this hafts for ay (a,. a...) e XV(N) & (bp.bxn-bon---) Efren) → S*Cbiskon ---) = (ob.be..) Bence adfaint of s is s* defined by S*:{{ND > Mang by 5* (C1, A2-) = (0,04, 92-*)