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

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SUMMARY

The discussion focuses on the behavior of an electron in a finite quantum well when its energy (E) exceeds the potential energy (V0). When E > V0, the wave function exists outside the well, indicating that the electron is in an unbound state. The general solution for the wave function in this scenario can be derived from the Schrödinger equation, which provides insights into the electron's behavior both inside and outside the potential well.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Schrödinger equation
  • Knowledge of potential wells and bound vs. unbound states
  • Basic concepts of wave functions in quantum systems
NEXT STEPS
  • Study the solutions of the Schrödinger equation for finite potential wells
  • Explore the concept of unbound states in quantum mechanics
  • Learn about the implications of wave functions in quantum tunneling
  • Investigate the effects of external energy sources on electron states
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Students and professionals in physics, particularly those studying quantum mechanics, as well as educators seeking to explain the behavior of electrons in 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 Schrödinger equation for E > V? That should give you a hint of what the general solution is like.
 

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