Understanding the Infinite Well Potential for Modeling Electron Bound to Atom

In summary, the infinite square well doesn't model anything physical, and the closest thing that it comes to modeling is a finite quantum well. The potential in the well increases with distance, and the electron is attracted to the nucleus.
  • #1
swain1
30
0
I am just trying to get my head round how this models the electron bound to an atom. I don't understand why the potential is zero in the well What physical case corresponds to the condition that V(x)=0 for all values of x?
Thanks
 
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  • #2
If V(x) = 0 for all x (as opposed to only inside the well), then you have a completely free particle, with no net force acting on it. Is that what you were after, or did I misunderstand your question?
 
  • #3
Yes it was, that is what I thought it would be but then I was wondering why the potential could be zero inside the well as this is meant to represent a bound particle.
Also for a completely free particle, would there be a restriction on the value of n? cheers
 
  • #4
If the electron is in a box with impenetrable walls, then it's equivalent to being in an infinite potential well, in this case with V=0 inside. That is, the problem describes an electron confined to a finite region of space with the only forces acting during collisions with the walls.

Regards,
Reilly Atkinson
 
  • #5
The infinite square well doesn't really model anything physical. The closest thing that it comes to modeling is a finite quantum well used in semiconductor lasers. However, the square well is basically the simplest test case that you can construct in QM, since it illustrates the quantization of energy levels.
 
  • #6
What u might be looking for is the schrödinger equation expressed in radius and angle. You can then make a much more accurate picture as you can use the attraction of the electron to the nucleus as the potenital in the from U(x)= -ke^2 /r. This gives a much more accurate picture of an electron round an atom, as the potential isn't infinite or 0, but increases with distance. Hope this helps.
 

Related to Understanding the Infinite Well Potential for Modeling Electron Bound to Atom

1. What is an infinite well potential?

An infinite well potential is a theoretical construct used in quantum mechanics to model the behavior of a particle confined to a finite region. In this model, the potential energy within the well is constant and infinite, while outside the well it is zero.

2. How is the infinite well potential used to model an electron bound to an atom?

The infinite well potential is used to model the electron's behavior within the atom's nucleus. The electron is considered to be confined within the potential well created by the positive charge of the nucleus. This model allows for the calculation of the electron's energy levels and probability of being in a certain location within the atom.

3. What are the limitations of using the infinite well potential to model an electron?

The infinite well potential model is a simplified representation and does not take into account the effects of other particles and forces within the atom, such as electron-electron interactions and the effects of relativity. It also assumes a perfectly spherical and static nucleus, which is not always the case in reality.

4. How does the infinite well potential model explain the stability of atoms?

In the infinite well potential model, the electron is confined within the potential well created by the nucleus, which prevents it from escaping. This confinement leads to discrete energy levels for the electron, which correspond to the electron's stability within the atom. The lower the energy level, the more stable the electron is within the atom.

5. Can the infinite well potential model be applied to other particles besides electrons?

Yes, the infinite well potential model can be used to model the behavior of other particles, such as protons and neutrons, within an atom. However, the specific values for the potential well and energy levels will differ for each type of particle due to their different masses and charges.

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