5. The Hamiltonian due to the interaction of a particle (mass m, charge q, and spin S) with a magnetic field pointing al

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5 The Hamiltonian Due To The Interaction Of A Particle Mass M Charge Q And Spin S With A Magnetic Field Pointing Al 1 (66.54 KiB) Viewed 24 times

5. The Hamiltonian due to the interaction of a particle (mass m, charge q, and spin S) with a magnetic field pointing along the y-axis is Ĥ =-9B -S, - S,. (a) Find the equations of mc motion for operators S, S, and S. in Heisenberg picture, i.e., dSH (1) dSH (1) and " dt dt dSH (1) (b) Solve these equations to obtain the components of the spin operators S(1), dt SH (1), SH (1) as functions of time in Heisenberg picture (Hint: the general solution of d² Â -+0²A=0 is A(t) = A(0)e and A₁ (0) = A) (15 points). dt²