Question

Problem 2 The time evolution of a spin-$j$ particle is governed by the Hamiltonian $\hat{H} = -\mu \hat{B} \cdot \hat{J} = -\mu |B| \hat{n} \cdot \hat{J}$. (4) (a) Write down the Heisenberg equation of motion for $\hat{J}$. (b) Show that the spin precession frequency does not depend on $j$.

          Problem 2 The time evolution of a spin-$j$ particle
is governed by the Hamiltonian
$\hat{H} = -\mu \hat{B} \cdot \hat{J} = -\mu |B| \hat{n} \cdot \hat{J}$.
(4)
(a) Write down the Heisenberg equation of motion
for $\hat{J}$.
(b) Show that the spin precession frequency does
not depend on $j$.

Problem 2 The time evolution of a spin-j particle
is governed by the Hamiltonian
Ĥ = -μB̂·Ĵ = -μ |B| n̂·Ĵ.
(4)
(a) Write down the Heisenberg equation of motion
for Ĵ.
(b) Show that the spin precession frequency does
not depend on j.

Added by Charles F.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Dominador Tan

12/12/2023

Step 1

Step 1: The Heisenberg equation of motion for an operator A is given by the equation of motion dA/dt = (i/hbar) [A, H], where [A, H] denotes the commutator of A and H. Show more…

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Problem 2 The time evolution of a spin- j particleProblem 2 The time evolution of a spin- j particle is governed by the Hamiltonian hat(H)=-mu B*hat(J)=-mu |B|hat(n)*hat(J). (a) Write down the Heisenberg equation of motion for hat(J). (b) Show that the spin precession frequency does not depend on j. is governed by the Hamiltonian hat(H)=-mu B*hat(J)=-mu |B|hat(n)*hat(J). (a) Write down the Heisenberg equation of motion for hat(J). (b) Show that the spin precession frequency does not depend on j. Problem 2 The time evolution of a spin-i particle is governed by the Hamiltonian H=-B.J=-|B|n.J (4) (a) Write down the Heisenberg equation of motion for J. (b) Show that the spin precession frequency does not depend on j.