In a one-dimensional problem, consider a particle of potential energy V(X) = -fX, where f is a positive constant [V(X) arises, for example, from a gravity field or a uniform electric field].
a. Write Ehrenfest's theorem for the mean values of the position X and the momentum P of the particle. Integrate these equations, compare with the classical motion.
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The solution demonstrates, step-by-step, how to use Ehrenfest theorem to find and solve the equation of motion for a particle in a constant force field.