Finite quantum well, multiple choice question

[Theodore0101]

Homework Statement

Consider an electron trapped in a one-dimensional finite well of width L. What is the minimum possible kinetic energy of the electron?

A) 0

B) Between 0 and h^2/8mL^2

C) ≈h^2/8mL^2, but it is not possible to find the exact value because of the uncertainty principle

D) Exactly h^2/8mL^2

Relevant Equations

E=n^2 *h^2/8mL^2

Homework Statement:: Consider an electron trapped in a one-dimensional finite well of width L. What is the minimum possible kinetic energy of the electron?

A) 0

B) Between 0 and h^2/8mL^2

C) ≈h^2/8mL^2, but it is not possible to find the exact value because of the uncertainty principle

D) Exactly h^2/8mL^2
Homework Equations:: E=n^2 *h^2/8mL^2

Hi!

I think I can rule out A) since if there is no kinetic energy the velocity must be 0, therefor there is no momentum, and then no uncertainty of momentum. Because of the uncertainty principle the uncertainty of position would therefor be infinitive, and we require the electron to be within L, so that wouldn't work.

I know that the lowest energy has something to do with h^2/8mL^2 since that's what the state n=1 gives, but all of the remaining options have a connection to it and I'm not sure from here.

Thanks

 

[Abhishek11235]

Hint:
An alternate question: What is minimum possible energy of electron in the box? Can you answer this?

 

[Theodore0101]

Hint:
An alternate question: What is minimum possible energy of electron in the box? Can you answer this?

The least amount of energy it can have is h^2/8mL^2, right? Is all the energy kinetic energy? Is that the answer?

 

[Abhishek11235]

Yes. This is the minimum kinetic energy the particle can possess(If you work in the realm of non relativistic QM