Bad Qubits — Learn Quantum by Doing

Multiple choice

Ehrenfest's theorem for the average position and momentum of a particle gives d/dt <p> = -<dV/dx>. Why is this not exactly Newton's law d/dt p = -V'(<x>)?

It contains the average of the force, <V'(x)>, not the force evaluated at the average position, V'(<x>); these differ unless V is at most quadratic
Momentum is never conserved in quantum mechanics, so the right-hand side is meaningless
The expectation value of momentum is always zero, making both sides vanish
It is off by a factor of hbar that survives in the classical limit