Question

quantum physics.

no one is solvong it right

please solve it.

from a) to h)

step by step.

Consider a spin-1 particle placed in a constant uniform magnetic field along the z-axis. The particle is initially in the state 11,0> of the S, operator. a) Find the state at a later time t. b) Find <S> at initially. c) Find <$,> at time t. d) Find <s> at time t. e) Find <S> at initially. f) Find <$.> at time t. g) Find the probability to have /1,-1> of $ at time t. h) Find the probability to have 71,-1> of $ (y-component of $ )at time t.

Answer 1

Auf- Â =-MABS = -MeBo $(38= Bî) At t=0, particle is in 11,0% (eigenstade of Sse operator) particle is a spinal pandicle, il, sal, my=-1, 0, 1. Baris me : {!!, 1), 11,02:11, -23. (Hamiltonian baris same asse) Su = = ($+ +$.) ; $y = K ($t -S.) ; § 18, mi) = mstilbima? & Isims> = [s(s+1) - Ms (ms +1) ħ 11, mstl> ; § ²1s, mx) = x(+1) hiking Ŝ. | ., mw = s(A+1) – mg (max-1) th 14, ms-1) 1 tl 11,1) 11,0) 11,-1) § III) 11,07 11,-1) Ś= (1,11 | o with 0 S_=(1,111 0 0 0 (1,01 o o fat <1,01 Fat 0 0 <1,-1) • 0 0 <1,-110 S2th o SA 111,1) 11,0) 11, -1) $2 11,111,0) 11,-1) SE (1,1)] 0 0. SP =,111 2*2 0 0 <1,011 0 0 0 <1011 o {1,-11 o o h < 1 24? + lot ol Sox = 1/2 (st 1 0 1 Baris of $ ! 11 = (): 11,02= 1), 11,-1)= () Eigenvalues of sai 1sx-21/20.. 1-2 tse ol Itse -Hsz 20 = - 10° to - ZO. for îmo, lots olla. I to tlan 1 : Hotsz 01 26-32+ ) 20 > 2=0,37] ) » K250], [W, 3 Mg] *I 12.1992= $(1) - last CSscanned with CamScanner

tuet RD (a) Energy eigenvalues of Hamiltonian, IH-EI) 20. · |-Mg Bato - e 0 0 0 - E 30 % E = -MeBo to 0 -E+Mg Botil E. E, =-Me Both with eigen vechera 11,125 (?). E = 0 with eigen vector 11,072=(:). Ez = Mg Bot with eigenvector 11,-1) 19). :o 11,0%) = 11,1) e-Ett - W ve lo I o I-1] I SE, = Mg Boh 11034) = ba le 28/11,12 - eTest/# 11, -1) 7 1/2) Aug ( Ez = Mg Boh (b) (59= 3,01 11.9% = 4(10 -1). (2016) - O -1) () =0. |-• {$x) = ($1750 law 183 (Sun = 31,04) $ /1,714) - the leve Va t 1) - e i5 +4,-1). Z to lo lo! Śli ola e-i£gt/ (elite o pist/1) Le e-15,t/th e-iegt/t = 0. 3. <Šm2 = 0. James CSScanned with CamScanner

(d) (32) =4<1,0|82|1,0%(4) all = (CLEAR VIl-pitting, -1) 32 (piesta 1,- exista 1-2) = [ (inte mi) - pi fila, L, -1) 2*2 (E FA A 1,2 - 150 ->) = 3x25* ** . {$P>= *** J As X2 (C) <372 510l $41!0= { $ol - Şu+1) S (19,13 - 19,-)) = ($0,- x,-1) (+117% + 11,-) = ( #-0 +0-*) = 0. 0. (8) (8) = (4) £1,01 $11,0%) = 1 Corinteni - . -1) (eitit 1.DE (t-t) =0. teiest/? t 1-1 13) o fem -h, Isu-AI120. ħ ra o 77,7 €162 h treo lo hlarz ħ J123] + *₂ + zod .::19,-123 + (-a) = (12=5 /103*11-13) Probability, p=1,-1|1,0742) * = lil: il - faşı,ol + şey bile ve dhe y - Live (e-19,44_priest/M)]= /1-2216 video Cena wafp = (a- 2 cas () = { sina (E39as i (E3-E)t/ CScann ed with CamScanne Saus. [E = -4B Bok)

(h) lo 52-ti I 22 1-12h o 10-Ft A: - to o 52 til = 0 11 12 13 | 1 0 o 1 о то for => 1, - 50 ; + =0.p0,2=73 1742 + ola -0. 2 >> ac-7131 A₂ = √2 x, [laz-izli =ļ (11,1)2 - |1,07 - 11,-1) co Probability, P = 15-111,05438 - PE 3 (3,11+i vzg1,01 - 31-1). La lelut 1,0) - test thin-Y 1 | 62€,tft + elegt/p2 = (atelle,-E)+44 et 65-614) (1+ cas (6-EM) = * (** West (1994--) iP = cos? ("*24) = { cos? (2xzbot) ] 3-kg = Mo Byt ? Aus? E, = - Mg Bot} CScanned with CamScanner