Help with quantum problem (gravitational field)

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SUMMARY

The discussion focuses on finding the energy spectrum of photons transitioning to the 1st excited state of a neutron in a gravitational field with a strength of 9.8 m/s². The key steps involve determining the potential energy function U(x) and substituting it into the Schrödinger equation. The use of Airy functions is highlighted as relevant due to their connection with the differential equation derived from the Schrödinger equation. Understanding the similarities between these equations is crucial for solving the problem.

PREREQUISITES
  • Understanding of the Schrödinger equation
  • Knowledge of potential energy in gravitational fields
  • Familiarity with Airy functions
  • Basic principles of quantum mechanics
NEXT STEPS
  • Research the derivation of potential energy functions in gravitational fields
  • Study the application of Airy functions in quantum mechanics
  • Explore solving the Schrödinger equation for different potential energy scenarios
  • Investigate energy level transitions in quantum systems
USEFUL FOR

Students and researchers in quantum mechanics, physicists working on gravitational effects in quantum systems, and anyone interested in the application of mathematical functions in physics.

eku_girl83
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I need to find the energy spectrum for the energes of photons that end up in the 1st excited state from a neutron in a gravitational field of strength g (9.8). I suppose first I need to find an expression for U(x) and substitue into the Schrödinger equation? How do I know U(x)? We have been using Airy functions in class -- how do I apply these here?

I guess I just need someone to get me started on this one with a hint or two!
 
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To find the energy levels of a particle in a gravitational field, you must solve the Schrödinger equation with the appropriate potential. Now I know you know what the potential energy of a particle in a gravitational field is. Don't think too hard, this is basic classical mechanics. The connection to Airy functions comes from looking at the differential equation they solve and comparing it to the Schrödinger equation you have written down. Do you notice any similarities?
 

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