Learning Path
Question & Answer1
Understand Question2
Review Options3
Learn Explanation4
Explore TopicChoose 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
Practice Similar Questions
Test your understanding with related questions
1
Question 1Which of the following statements correctly describe key milestones in the development of quantum mechanics? (Select all that apply)
hardComputer-science
Practice
2
Question 2Ehrenfest's theorem : Classical Mechanics :: Schrodinger's wave equation : ?
mediumComputer-science
Practice
3
Question 3A 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
4
Question 4Which statement best describes the evolution of a quantum state according to Ehrenfest's theorem?
easyComputer-science
Practice
5
Question 5Which of the following statements about quantum state dynamics are true? (Select all that apply)
mediumComputer-science
Practice
6
Question 6How does Ehrenfest's theorem relate classical and quantum mechanics in the context of a quantum state's evolution?
mediumComputer-science
Practice
7
Question 7Which of the following statements correctly describe key milestones in the development of quantum mechanics? (Select all that apply)
hardComputer-science
Practice
8
Question 8A 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
9
Question 9Which of the following statements about quantum state dynamics are true? (Select all that apply)
mediumComputer-science
Practice
10
Question 10How 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.