Finite Quantum Well: Wave Function when E>V{0}?

In summary, the conversation discusses the appearance of the wave function for an electron in a finite quantum well with an energy greater than the potential. The question is raised about whether the wave function exists above the well, and it is explained that such states do exist for unbound electrons. The suggestion is made to look at the Schrodinger equation for energy greater than the potential for a better understanding of the general solution.
  • #1
KingBigness
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Homework Statement



If an electron is in a finite quantum well and it's E>V{0} what does the wave function look like?

Homework Equations





The Attempt at a Solution



Wondering if anyone could help me out with this?
I know that outside the well the electron will have the same general solution as that of an electron inside the well when E<V{0}...but what does the electron inside the well look like when E>{0}?

Does the wave function exist above the well? Does that even make sense?
 
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  • #2
If an electron is not inside a potential well it is called 'unbound', and yes such states exist! An atom is a potential well, and if you provide enough energy to one of the electrons (for example by firing a photon at it) you can eject it from the atom, and it becomes unbound.

What is the form of schrodinger equation for E > V? That should give you a hint of what the general solution is like.
 

1. What is a finite quantum well?

A finite quantum well is a physical system in which a particle, such as an electron, is confined to a limited space by potential barriers on either side. This creates a well-like structure where the particle's energy is quantized.

2. How does the wave function change when the energy of the particle is greater than the potential energy barrier?

When the energy of the particle is greater than the potential energy barrier, the wave function extends beyond the barriers and becomes a decaying exponential. This means that there is a small probability of finding the particle outside of the well.

3. What happens to the wave function when the energy of the particle is less than the potential energy barrier?

When the energy of the particle is less than the potential energy barrier, the wave function becomes evanescent and does not extend beyond the barriers. This means that the particle is completely confined within the well and cannot escape.

4. How does the width of the potential well affect the behavior of the wave function?

The width of the potential well directly affects the energy levels and allowed states of the particle. A wider well will have more energy levels and allow for more possible states, while a narrower well will have fewer energy levels and a smaller range of allowed states.

5. Can the finite quantum well model be applied to other systems besides particles?

Yes, the finite quantum well model can be applied to other physical systems, such as atoms and molecules. It can also be used to study the behavior of quantum dots and other nanostructures.

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