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

If you connect a 1.8 F and a 2.6 F capacitor in series, what will be the equivalent capacitance?

Suppose that a particular heart defibrillator uses a 1.5 x 10-5 Farad capacitor. If it is charged up to a voltage of 7300 volts, how much energy is stored in the capacitor? Give your answer as the number of Joules.

The voltage difference across an 8.3 nanometer thick cell membrane is 6.5 x 10-5volts. What is the magnitude of the electric field inside this cell membrane? (Assume the field is uniform, and give your answer as the number of Volts per meter... which is the same as the number of Newtons per Coulomb.)

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