Question

onsider state 5pace, Physeed System whse an three dimensinnal, is spaned by Whic h s or tho norma basis 5 1u,>, 1u In This basis tiHamiltenian opert an H of t system and or observable written are 2 A a 2 Positive real Constant s Where w, and a a re 3 in the s tate at time tn physical syste T 2 2 2 shous that. < 1E,>- S 2 V/2 n T nl T 2 Satisfy H w, are The hree eiqenvector 5 of H that Scanned with deteraed their associated e igenvalu es En- E,w.

Answer 1

G ) - i 2 K'31 H wo 1. C 2 1+0 i-2i+0 2 HlE,) 90 2 H EY 2 - C C 2++0 i+21+0 3h 0o 3 wo Es) #1) o o O O

() 1 2, A cut (A-1) Figevaluu A> -2) (-1-0 - i - -2 1,1, dn=a,0,- igeugutiouo Comopouding Alan dnldny 1 1 OO a -1 D @ 0 0 ib-C () f2 1u,

3. o)L u,y (u,+ u,y 2 2 2 , liy b, 1,b, l'sy 4 b3 -i b,- bs ibi ibs V2 2 2 $3 bb bs 2 2 2 b,1-i 2/2 A (+ 2b, = 1+1 2bs 22 1- 1, + 22 l,+ +1 145y 1Uio>> 22 1+1 Ax 2 Plat)-1 4 22 P) 2 2 S2

4. Lowu- posib valut 1g(o)> Correopondivg sigeutat 1s + -i3w,t -iwt iu2y e 19t) + 6. Whn 2We -is 1/2 -in/2 1() 2We T 1227 ju3 = 10-(12-18,) 21 1u2 IEs-1E 2 1e,y18,u D 2 P(e) P(2,) 2 1