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Quantum State Dynamics
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Which statement best describes the evolution of a quantum state according to Ehrenfest's theorem?

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Choose the Best Answer

A

It follows classical mechanics principles exactly.

B

It evolves according to the wave function and operators.

C

It is independent of external forces acting on the system.

D

It cannot be predicted over time.

Understanding the Answer

Let's break down why this is correct

Answer

Ehrenfest's theorem says that the average position and momentum of a quantum particle follow the same equations of motion as a classical particle, but only for the mean values. The theorem links the time derivative of the expectation value of an observable to the expectation value of its commutator with the Hamiltonian. Thus, while the quantum state itself evolves according to Schrödinger’s equation, its statistical averages obey Newton’s laws. For example, an electron in a constant electric field will have its average position accelerate exactly like a classical charge, even though its wave function spreads out over time. This shows that quantum mechanics reproduces classical dynamics for expectation values.

Detailed Explanation

Ehrenfest's theorem shows that the average value of a quantum observable follows the same rule as a classical variable. Other options are incorrect because The misconception is that quantum motion is identical to classical motion; The misconception is that forces do not affect quantum evolution.

Key Concepts

Quantum State Dynamics
Ehrenfest's Theorem
Wave Function
Topic

Quantum State Dynamics

Difficulty

easy level question

Cognitive Level

understand

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