10 3. A particle with total spin quantum number s is in the state with the highest z-componentof angular momentum (m=+s) at time t = 0. The particle is in a magnetic field and isgoverned by the Hamiltonian operator H=wS. You will find it useful to remember thatS. = S, +iS, and S = S, - iSy. Also, S+s, m) = √s(s+1) − m(m + 1) |s, m+ 1)and S. s. m) = h√√/s(s+1)-m(m-1) |s, m - 1).(a) At a very short time later, t = 8t, what is the probability, to lowest order in it, thatone would measure a value ms?(b) Again assuming small ót, the probability, to lowest order in St, of finding the particlein the m= -s state is proportional to what power of St?

Spin number of an atom tells us about the direction of spin of electron.The value of spin quantum…

3. A particle with total spin quantum number s is in the state with the highest z-component of angular momentum (m= +s) at time t= 0. The particle is in a magnetic field and is governed by the Hamiltonian operator H=wS,. You will find it useful to remember that S. = S,+iS, and S... S.- ¡Sy. Also, S, s, m) = h√s(s+1)-m(m+1) s. m+ 1) and S. Is, m) = h√√/s(s+1)-m(m-1) |s, m-1). (a) At a very short time later, t = 8t, what is the probability, to lowest order in it, that one would measure a value ms? (b) Again assuming small &t, the probability, to lowest order in St, of finding the particle in the m= -s state is proportional to what power of St?