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?
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?
Principles of Instrumental Analysis
7th Edition
ISBN:9781305577213
Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Chapter6: An Introduction To Spectrometric Methods
Section: Chapter Questions
Problem 6.1QAP
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