Infinite Square-Well Potential Problem

[interxavier]

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.

 

[vela]

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.

 

[interxavier]

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?

 

[vela]

Relate the energy of the emitted photons to the energy of the electron.

 

[interxavier]

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?

 

[vela]

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?