(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Quantum mechanics is absolutely confusing me.

A proton is confined in an infinite square well of length 10^{-5}nm.

Calculate the wavelength and energy associated with the photon that is emitted when the proton undergoes a transition from the first excited state (n=2) to the ground state (n=1).

In what region of the electromagnetic spectrum does this wavelength belong?

3. The attempt at a solution

I'm not really sure what I'm doing at all.

But I started with the time independent Schrodinger equation. For region I and III, (where the potential is infinite) then the eigenfunction must be 0.

So I put in a potential of zero for the second region and got

[itex]\frac{d^2\psi}{dx^2} + k^2\psi = 0[/itex] where [itex]k^2 = \frac{2mE}{\hbar}[/itex]

Looks like a second order diff eq, so I tried to solve it. Solutions to the characteristic equation were ±ik...

From here I am a little stumped, I didn't take notes, and I can't remember what the solution was that he used in class.

But anyway if I'm just going by my normal diff eq understanding,

[itex]\psi = Acos(kx)+Bsin(kx)[/itex]

What's throwing me off is that I recall he had exponential solutions with imaginary components in them. These would oscillate, and so does my solution, but even if I had my solution in his form, what next?

Where does the length of the well come into play? What does n=2 -> n=1 mean?

Am I making this more complicated than it should be?

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# Homework Help: Finding the eigen function for an infinite square well (quantum mechanics)

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