Why a particle confined to a finite region cannot have zero energy.

Question

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Answer 1

Question

Chapter 35, Problem 1FTD

To determine

Why a particle confined to a finite region cannot have zero energy.

Expert Solution & Answer

Explanation of Solution

If the ground state-state energy of a particle that confined to a finite region is zero, then it will violate the uncertainty principle. Because of the zero kinetic energy, the particle has zero momentum and then its position is absolutely determined.

That means the uncertainty in position is equal to the width of the potential well (region), then the uncertainty relation becomes ΔpΔx=0 . The statistical nature of the quantum mechanics is lost and the uncertainty principle ΔpΔx≥ℏ

Therefore, the particle confined to a finite region cannot have zero energy.

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Answer 2

Question

Chapter 35, Problem 1FTD

To determine

Why a particle confined to a finite region cannot have zero energy.

Expert Solution & Answer

Explanation of Solution

If the ground state-state energy of a particle that confined to a finite region is zero, then it will violate the uncertainty principle. Because of the zero kinetic energy, the particle has zero momentum and then its position is absolutely determined.

That means the uncertainty in position is equal to the width of the potential well (region), then the uncertainty relation becomes ΔpΔx=0 . The statistical nature of the quantum mechanics is lost and the uncertainty principle ΔpΔx≥ℏ

Therefore, the particle confined to a finite region cannot have zero energy.

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Answer 3

Question

Chapter 35, Problem 1FTD

To determine

Why a particle confined to a finite region cannot have zero energy.

Expert Solution & Answer

Explanation of Solution

If the ground state-state energy of a particle that confined to a finite region is zero, then it will violate the uncertainty principle. Because of the zero kinetic energy, the particle has zero momentum and then its position is absolutely determined.

That means the uncertainty in position is equal to the width of the potential well (region), then the uncertainty relation becomes ΔpΔx=0 . The statistical nature of the quantum mechanics is lost and the uncertainty principle ΔpΔx≥ℏ

Therefore, the particle confined to a finite region cannot have zero energy.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 35, Problem 1FTD

To determine

Why a particle confined to a finite region cannot have zero energy.

Expert Solution & Answer

Explanation of Solution

If the ground state-state energy of a particle that confined to a finite region is zero, then it will violate the uncertainty principle. Because of the zero kinetic energy, the particle has zero momentum and then its position is absolutely determined.

That means the uncertainty in position is equal to the width of the potential well (region), then the uncertainty relation becomes ΔpΔx=0 . The statistical nature of the quantum mechanics is lost and the uncertainty principle ΔpΔx≥ℏ

Therefore, the particle confined to a finite region cannot have zero energy.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 35, Problem 1FTD

To determine

Why a particle confined to a finite region cannot have zero energy.

Expert Solution & Answer

Explanation of Solution

If the ground state-state energy of a particle that confined to a finite region is zero, then it will violate the uncertainty principle. Because of the zero kinetic energy, the particle has zero momentum and then its position is absolutely determined.

That means the uncertainty in position is equal to the width of the potential well (region), then the uncertainty relation becomes ΔpΔx=0 . The statistical nature of the quantum mechanics is lost and the uncertainty principle ΔpΔx≥ℏ

Therefore, the particle confined to a finite region cannot have zero energy.

Answer 6

Chapter 35, Problem 1FTD

To determine

Why a particle confined to a finite region cannot have zero energy.

Expert Solution & Answer

Explanation of Solution

If the ground state-state energy of a particle that confined to a finite region is zero, then it will violate the uncertainty principle. Because of the zero kinetic energy, the particle has zero momentum and then its position is absolutely determined.

That means the uncertainty in position is equal to the width of the potential well (region), then the uncertainty relation becomes ΔpΔx=0 . The statistical nature of the quantum mechanics is lost and the uncertainty principle ΔpΔx≥ℏ

Therefore, the particle confined to a finite region cannot have zero energy.

Answer 7

Chapter 35, Problem 1FTD

To determine

Why a particle confined to a finite region cannot have zero energy.

Answer 8

Expert Solution & Answer

Explanation of Solution

If the ground state-state energy of a particle that confined to a finite region is zero, then it will violate the uncertainty principle. Because of the zero kinetic energy, the particle has zero momentum and then its position is absolutely determined.

That means the uncertainty in position is equal to the width of the potential well (region), then the uncertainty relation becomes ΔpΔx=0 . The statistical nature of the quantum mechanics is lost and the uncertainty principle ΔpΔx≥ℏ