Energy Quantization

Matter waves and energy quantization?

A proton confined in a one-dimensional box emits a 2.0 MeV gamma-ray photon in a quantum jump from n=2 to n=1.

What is the length of the box?
Would I have to use the mass of 2 protons since it's a gamma ray?
Oh nevermind...

Particle in a box is solved in every basic QM text--even wiki has it:

http://en.wikipedia.org/wiki/Particle_in_a_box

The solution is:
En = (pi^2 h-bar^2 / 2mL^2) n^2

So the energy of the gamma is:
E = E2 - E1 = (pi^2 h-bar^2 / 2mL^2)(2^2-1^2)

Solve for the length of the box:
L = sqrt (3 pi^2 hbar^2 / 2mE)

They give you the energy. You can look up planck's constant (reduced) and the mass of the proton. Plugnchug.

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