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Consider the case of particle in a 3d box and a 3d harmonic oscillator.
- a)The ground state wave function of a simple harmonic oscillator is a Gaussian
- b)The ground state energy of 3d simple harmonic oscillator is non zero
- c)The energy of the ground state of a 3d harmonic oscillator is zero.
- d)The ground state energy of a particle in a 3d box is non zero
Correct answer is option 'B,D'. Can you explain this answer?
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Consider the case of particle in a 3dbox and a 3dharmonic oscillator.a...
(For Harmonic Oscillator)
The correct answers are: The ground state energy of 3d simple harmonic oscillator is non zero, The ground state energy of a particle in a 3d box is non zero.
Most Upvoted Answer
Consider the case of particle in a 3dbox and a 3dharmonic oscillator.a...
Particle in a 3D Box:
- In the case of a particle in a 3D box, the wave function is given by the product of three separate wave functions, each corresponding to one dimension.
- The ground state wave function for each dimension is a sinusoidal function (sine or cosine).
- The energy of the ground state is given by the sum of the energies in each dimension, which is non-zero.
3D Harmonic Oscillator:
- The ground state wave function of a 3D harmonic oscillator is a Gaussian function.
- This is because the potential energy of a harmonic oscillator follows a quadratic form, leading to a Gaussian probability distribution for the particle's position.
- The energy of the ground state is non-zero because the particle still possesses kinetic energy even at the lowest energy level.
Comparison:
- The ground state wave function of a simple harmonic oscillator is a Gaussian, while the ground state wave function of a particle in a 3D box is a product of sinusoidal functions.
- The energy of the ground state of a 3D harmonic oscillator is non-zero because it includes both potential and kinetic energy contributions.
- In contrast, the energy of the ground state of a particle in a 3D box is non-zero solely due to the kinetic energy of the particle.
Conclusion:
Based on the above explanations, options B, C, and D are correct:
- The ground state energy of a 3D simple harmonic oscillator is non-zero.
- The energy of the ground state of a 3D harmonic oscillator is zero.
- The ground state energy of a particle in a 3D box is non-zero.
- In the case of a particle in a 3D box, the wave function is given by the product of three separate wave functions, each corresponding to one dimension.
- The ground state wave function for each dimension is a sinusoidal function (sine or cosine).
- The energy of the ground state is given by the sum of the energies in each dimension, which is non-zero.
3D Harmonic Oscillator:
- The ground state wave function of a 3D harmonic oscillator is a Gaussian function.
- This is because the potential energy of a harmonic oscillator follows a quadratic form, leading to a Gaussian probability distribution for the particle's position.
- The energy of the ground state is non-zero because the particle still possesses kinetic energy even at the lowest energy level.
Comparison:
- The ground state wave function of a simple harmonic oscillator is a Gaussian, while the ground state wave function of a particle in a 3D box is a product of sinusoidal functions.
- The energy of the ground state of a 3D harmonic oscillator is non-zero because it includes both potential and kinetic energy contributions.
- In contrast, the energy of the ground state of a particle in a 3D box is non-zero solely due to the kinetic energy of the particle.
Conclusion:
Based on the above explanations, options B, C, and D are correct:
- The ground state energy of a 3D simple harmonic oscillator is non-zero.
- The energy of the ground state of a 3D harmonic oscillator is zero.
- The ground state energy of a particle in a 3D box is non-zero.
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Consider the case of particle in a 3dbox and a 3dharmonic oscillator.a)The ground state wave function of a simple harmonic oscillator is a Gaussianb)The ground state energy of 3d simple harmonic oscillator is non zeroc)The energy of the ground state of a 3d harmonic oscillator is zero.d)The ground state energy of a particle in a 3d box is non zeroCorrect answer is option 'B,D'. Can you explain this answer?
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Consider the case of particle in a 3dbox and a 3dharmonic oscillator.a)The ground state wave function of a simple harmonic oscillator is a Gaussianb)The ground state energy of 3d simple harmonic oscillator is non zeroc)The energy of the ground state of a 3d harmonic oscillator is zero.d)The ground state energy of a particle in a 3d box is non zeroCorrect answer is option 'B,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 case of particle in a 3dbox and a 3dharmonic oscillator.a)The ground state wave function of a simple harmonic oscillator is a Gaussianb)The ground state energy of 3d simple harmonic oscillator is non zeroc)The energy of the ground state of a 3d harmonic oscillator is zero.d)The ground state energy of a particle in a 3d box is non zeroCorrect answer is option 'B,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 case of particle in a 3dbox and a 3dharmonic oscillator.a)The ground state wave function of a simple harmonic oscillator is a Gaussianb)The ground state energy of 3d simple harmonic oscillator is non zeroc)The energy of the ground state of a 3d harmonic oscillator is zero.d)The ground state energy of a particle in a 3d box is non zeroCorrect answer is option 'B,D'. Can you explain this answer?.
Consider the case of particle in a 3dbox and a 3dharmonic oscillator.a)The ground state wave function of a simple harmonic oscillator is a Gaussianb)The ground state energy of 3d simple harmonic oscillator is non zeroc)The energy of the ground state of a 3d harmonic oscillator is zero.d)The ground state energy of a particle in a 3d box is non zeroCorrect answer is option 'B,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 case of particle in a 3dbox and a 3dharmonic oscillator.a)The ground state wave function of a simple harmonic oscillator is a Gaussianb)The ground state energy of 3d simple harmonic oscillator is non zeroc)The energy of the ground state of a 3d harmonic oscillator is zero.d)The ground state energy of a particle in a 3d box is non zeroCorrect answer is option 'B,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 case of particle in a 3dbox and a 3dharmonic oscillator.a)The ground state wave function of a simple harmonic oscillator is a Gaussianb)The ground state energy of 3d simple harmonic oscillator is non zeroc)The energy of the ground state of a 3d harmonic oscillator is zero.d)The ground state energy of a particle in a 3d box is non zeroCorrect answer is option 'B,D'. Can you explain this answer?.
Solutions for Consider the case of particle in a 3dbox and a 3dharmonic oscillator.a)The ground state wave function of a simple harmonic oscillator is a Gaussianb)The ground state energy of 3d simple harmonic oscillator is non zeroc)The energy of the ground state of a 3d harmonic oscillator is zero.d)The ground state energy of a particle in a 3d box is non zeroCorrect answer is option 'B,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
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Consider the case of particle in a 3dbox and a 3dharmonic oscillator.a)The ground state wave function of a simple harmonic oscillator is a Gaussianb)The ground state energy of 3d simple harmonic oscillator is non zeroc)The energy of the ground state of a 3d harmonic oscillator is zero.d)The ground state energy of a particle in a 3d box is non zeroCorrect answer is option 'B,D'. Can you explain this answer?, a detailed solution for Consider the case of particle in a 3dbox and a 3dharmonic oscillator.a)The ground state wave function of a simple harmonic oscillator is a Gaussianb)The ground state energy of 3d simple harmonic oscillator is non zeroc)The energy of the ground state of a 3d harmonic oscillator is zero.d)The ground state energy of a particle in a 3d box is non zeroCorrect answer is option 'B,D'. Can you explain this answer? has been provided alongside types of Consider the case of particle in a 3dbox and a 3dharmonic oscillator.a)The ground state wave function of a simple harmonic oscillator is a Gaussianb)The ground state energy of 3d simple harmonic oscillator is non zeroc)The energy of the ground state of a 3d harmonic oscillator is zero.d)The ground state energy of a particle in a 3d box is non zeroCorrect answer is option 'B,D'. Can you explain this answer? theory, EduRev gives you an
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