Learning Path
Question & Answer1
Understand Question2
Review Options3
Learn Explanation4
Explore TopicChoose 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 shows that the average position follows Newton's laws when forces act. Other options are incorrect because The idea that the particle’s position is fixed ignores quantum uncertainty; Collapse happens after measurement, not before.
Key Concepts
Quantum State Dynamics
Ehrenfest's Theorem
Wave-Particle Duality
Topic
Quantum State Dynamics
Difficulty
easy level question
Cognitive Level
understand
Practice Similar Questions
Test your understanding with related questions
1
Question 1A 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?
easyComputer-science
Practice
2
Question 2Which statement best describes the evolution of a quantum state according to Ehrenfest's theorem?
easyComputer-science
Practice
3
Question 3How does Ehrenfest's theorem relate classical and quantum mechanics in the context of a quantum state's evolution?
mediumComputer-science
Practice
4
Question 4Which statement best describes the evolution of a quantum state according to Ehrenfest's theorem?
easyComputer-science
Practice
5
Question 5How does Ehrenfest's theorem relate classical and quantum mechanics in the context of a quantum state's evolution?
mediumComputer-science
Practice
Ready to Master More Topics?
Join thousands of students using Seekh's interactive learning platform to excel in their studies with personalized practice and detailed explanations.