Physics Exam > Physics Questions > Consider the following statements about a har...
Start Learning for Free
Consider the following statements about a harmonic oscillator: -
1. The minimum energy of the oscillator is zero.
2. The probability of finding it is maximum at the mean position.
Which of the statement given above is/are correct ?
1. The minimum energy of the oscillator is zero.
2. The probability of finding it is maximum at the mean position.
Which of the statement given above is/are correct ?
- a)I only
- b)2 only
- c)both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Consider the following statements about a harmonic oscillator: -1. The...
We know that total energy
Most Upvoted Answer
Consider the following statements about a harmonic oscillator: -1. The...
Explanation:
Statement 1: The minimum energy of the oscillator is zero.
- This statement is incorrect. The energy of a harmonic oscillator is quantized, meaning it can only have certain discrete energy levels. The lowest energy level, known as the ground state, is not zero but rather a finite non-zero value. This is due to the zero-point energy, which is the minimum energy that a system can have even at absolute zero temperature. The ground state energy of a harmonic oscillator is given by E = (1/2)hω, where h is Planck's constant and ω is the angular frequency of the oscillator.
Statement 2: The probability of finding it is maximum at the mean position.
- This statement is also incorrect. The probability distribution of finding the oscillator at different positions is given by the wave function, which describes the quantum state of the system. For a harmonic oscillator in its ground state, the wave function is a Gaussian distribution centered around the mean position. However, the probability is not maximum at the mean position but rather decreases symmetrically as we move away from the mean. The probability is actually highest at the turning points of the oscillator, where it momentarily comes to rest before changing direction.
Conclusion:
- Both statements 1 and 2 are incorrect.
- The minimum energy of the oscillator is not zero but a finite non-zero value due to the zero-point energy.
- The probability of finding the oscillator is not maximum at the mean position but rather highest at the turning points.
Statement 1: The minimum energy of the oscillator is zero.
- This statement is incorrect. The energy of a harmonic oscillator is quantized, meaning it can only have certain discrete energy levels. The lowest energy level, known as the ground state, is not zero but rather a finite non-zero value. This is due to the zero-point energy, which is the minimum energy that a system can have even at absolute zero temperature. The ground state energy of a harmonic oscillator is given by E = (1/2)hω, where h is Planck's constant and ω is the angular frequency of the oscillator.
Statement 2: The probability of finding it is maximum at the mean position.
- This statement is also incorrect. The probability distribution of finding the oscillator at different positions is given by the wave function, which describes the quantum state of the system. For a harmonic oscillator in its ground state, the wave function is a Gaussian distribution centered around the mean position. However, the probability is not maximum at the mean position but rather decreases symmetrically as we move away from the mean. The probability is actually highest at the turning points of the oscillator, where it momentarily comes to rest before changing direction.
Conclusion:
- Both statements 1 and 2 are incorrect.
- The minimum energy of the oscillator is not zero but a finite non-zero value due to the zero-point energy.
- The probability of finding the oscillator is not maximum at the mean position but rather highest at the turning points.
Free Test
FREE
| Start Free Test |
Community Answer
Consider the following statements about a harmonic oscillator: -1. The...
We know that total energy
|
Explore Courses for Physics exam
|
|
Similar Physics Doubts
Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer?
Question Description
Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer?.
Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer?.
Solutions for Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following statements about a harmonic oscillator: -1. The minimum energy of the oscillator is zero.2. The probability of finding it is maximum at the mean position.Which of the statement given above is/are correct ?a)I onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup