Infinite Square-Well Potential Problem

  • #1

Homework Statement


An electron is trapped in an infinite square-well potential of width 0.5 nm. If the electron is initially in the n = 4 state, what are the various photon energies that can be emitted as the electron jumps to the ground state?


Homework Equations


The Schroedinger Equation:
-[STRIKE]h[/STRIKE]/2m*d^2Y/dx^2 + V*Y = E*Y

En = - Eo/n^2

The Attempt at a Solution



My understanding is that Y(0) = Y(L) = 0, making them the boundary conditions.

You need to find the solution for Y by solving the Schroedinger Eq'n, which is a Differential Equation.

I'm totally blank afterwards.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
vela
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Are you sure it's necessary to solve the infinite-square-well problem from scratch? It's probably solved in your textbook or notes, and you can use those results to solve this problem.
 
  • #3
Are you sure it's necessary to solve the infinite-square-well problem from scratch? It's probably solved in your textbook or notes, and you can use those results to solve this problem.

What am I supposed to do in this problem?
 
  • #4
vela
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Relate the energy of the emitted photons to the energy of the electron.
 
  • #5
Relate the energy of the emitted photons to the energy of the electron.

Okay, the energy of the electron, because it's in state 4, is E4 = -Eo/4^2. What about the photons? I know the energy of a photon is E = hf but how do I apply this to the problem?
 
  • #6
vela
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Well, figuring that out is the point of the problem. The emitted photon carries energy away, right? Where does the energy come from and what happens to the electron?
 

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