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

AI Thread Summary
In a finite quantum well where the energy E is greater than the potential V0, the wave function inside the well resembles that of a free particle, indicating that the electron is in a bound state. Outside the well, the wave function transitions to a form that reflects the unbound state, suggesting that the electron can exist beyond the potential barrier. The Schrödinger equation for E > V0 provides insight into the wave function's characteristics, which can be expressed as oscillatory rather than exponential decay. This indicates that the electron has enough energy to be unbound, similar to an electron ejected from an atom. Understanding these concepts is crucial for analyzing quantum behavior in finite potential wells.
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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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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.
 
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