Heisenberg and energy of an electron in a potential well

In summary, the conversation discusses using the uncertainty principle to estimate the ground state energy of an electron in a one dimensional potential well. The participant initially obtains a value in the order of 10^31, but upon revising their calculations with the correct units, they arrive at a more accurate estimate of 10^-21.
  • #1
CloudDreamer7
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[SOLVED] Heisenberg and energy of an electron in a potential well

Homework Statement


An electron is confined within a one dimensional potential well that measures 1 nm. using the uncertainty principle, estimate the order of magnitude for the ground state energy of the electron in the well in eV.


Homework Equations




The Attempt at a Solution



i used the equality in the uncertainty principle and substituted DeltaY (uncertainty in position) with 10^-9 m . Then you have only 1 unknown which is DeltaP_y (uncertainty in momentum y - component). I got a number from here and then used it in the expression of the KE in terms of momentum (P^2/2m = KE). unfortunately what i got was sth in the order of 10^31 which is surely wrong.

Any ideas ?
 
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  • #2
I got about 10^-21 with the same procedure. Try again and be carefull to use correct units.
 

FAQ: Heisenberg and energy of an electron in a potential well

What is Heisenberg's uncertainty principle?

The Heisenberg uncertainty principle is a fundamental concept in quantum mechanics that states that it is impossible to simultaneously determine the exact position and momentum of a particle. This means that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

How does the uncertainty principle relate to the energy of an electron in a potential well?

The uncertainty principle applies to the energy of an electron in a potential well because the energy of a particle is closely related to its momentum. Therefore, the more precisely we know the energy of an electron, the less precisely we can know its position within the potential well.

What is a potential well in quantum mechanics?

A potential well is a region in space where a particle is confined due to the presence of a potential energy barrier. This can be thought of as a "well" or "trap" that the particle is unable to escape from, similar to a ball rolling into a dip in a surface.

How does the size of a potential well affect the energy of an electron?

The size of a potential well directly affects the energy of an electron. A larger potential well allows for more possible positions and energies for the electron, resulting in a higher uncertainty in its energy. A smaller potential well, on the other hand, restricts the possible positions and energies of the electron, leading to a lower uncertainty in its energy.

Can the energy of an electron in a potential well ever be known exactly?

No, according to the uncertainty principle, the exact energy of an electron in a potential well can never be known. This is because the more precisely we know the energy, the less precisely we can know the position of the electron within the potential well. This fundamental uncertainty is a key principle in quantum mechanics.

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