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

Question

Want to see more full solutions like this?

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.

Want to see more full solutions like this?

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

Students have asked these similar questions

Give an explanation why the measurement of energy for many-electron atoms is not accurately calculated using mathematical analytical methods, variation methods and perturbation methods !

question 3 please

Imagine a proton confined in an infinitely square well of length 10 fm, atypical nuclear diameter. Calculate the energy and wavelength associatedwith the photon emitted when the proton moves from n = 2 state to theground state.

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.

Want to see more full solutions like this?

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

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.

Want to see more full solutions like this?

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.

Want to see more full solutions like this?

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