📚 Learning Guide
Quantum State Dynamics
easy

A physicist is analyzing a quantum system that exhibits wave-particle duality. They observe that the expectation value of the position of a particle evolves over time according to Ehrenfest's theorem. Which of the following statements best describes the implications of this observation in the context of quantum state dynamics?

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Choose the Best Answer

A

The particle's position is fixed and does not change over time.

B

The average position of the particle behaves like a classical particle under the influence of forces.

C

The particle's wave function collapses instantaneously upon measurement, preventing any prediction of its position.

D

The dynamics of the quantum system can be completely understood without considering external forces.

Understanding the Answer

Let's break down why this is correct

Answer

The observation means that, although the particle behaves quantum‑mechanically, its average position moves just like a classical particle would under the same forces, because Ehrenfest’s theorem links the quantum expectation values to Newton’s equations. This shows that the quantum state’s center follows a classical trajectory, while the spread of the wave packet still reflects quantum uncertainty. For instance, a Gaussian wave packet in a harmonic potential will have its mean position oscillate at the classical frequency, even though the packet’s width may change over time. Thus, the result highlights the correspondence between quantum dynamics and classical mechanics for expectation values, but it does not imply that the entire quantum state is classical.

Detailed Explanation

Ehrenfest's theorem links the average behavior of a quantum particle to the equations that govern a classical particle. Other options are incorrect because The misconception here is that a particle’s position can be frozen in time; This option mixes up wave function collapse with the prediction of expectation values.

Key Concepts

Quantum State Dynamics
Ehrenfest's Theorem
Wave-Particle Duality
Topic

Quantum State Dynamics

Difficulty

easy level question

Cognitive Level

understand

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