How Do Airy Function Roots Determine Photon Energies in a Gravitational Field?

[eku_girl83]

The situation involves a neutron in a constant gravitational field (g=9.8). I need to find the energies of photons that transition to the excited state. I solved the Schrödinger equation by doing a variable transformation using Airy functions. To fully solve, however, I need to find the roots of the Airy function. I looked these up in a table, but am unsure how they are related to the energy/wavelength I am trying to find. Do the roots (-2.33811, -4.08795, -5.52056,...) correspond to energies?
Is there another equation I use to get the energies? I recall the E = -13.6 eV (1/n1^2 - 1/n2^2) and E = hc/lambda equations from previous physics courses? Can I apply these here?

 

[Andrew Mason]

The situation involves a neutron in a constant gravitational field (g=9.8). I need to find the energies of photons that transition to the excited state. I solved the Schrödinger equation by doing a variable transformation using Airy functions. To fully solve, however, I need to find the roots of the Airy function. I looked these up in a table, but am unsure how they are related to the energy/wavelength I am trying to find. Do the roots (-2.33811, -4.08795, -5.52056,...) correspond to energies?
Is there another equation I use to get the energies? I recall the E = -13.6 eV (1/n1^2 - 1/n2^2) and E = hc/lambda equations from previous physics courses? Can I apply these here?

http://www.users.csbsju.edu/~frioux/neutron/neutron.htm" may help you.

AM