Help with quantum problem (gravitational field)

In summary, to find the energy spectrum for photons ending up in the 1st excited state from a neutron in a gravitational field, one must solve the Schrodinger equation with the appropriate potential, which can be found by applying basic classical mechanics. The use of Airy functions comes from comparing the differential equation they solve to the Schrodinger equation.
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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 Schrodinger 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 Schrodinger 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 Schrodinger equation you have written down. Do you notice any similarities?
 

1. What is the gravitational field in quantum mechanics?

In quantum mechanics, the gravitational field is described by the theory of quantum gravity, which attempts to reconcile the principles of quantum mechanics with those of general relativity. It is believed that at the quantum level, gravity is mediated by particles called gravitons, which interact with matter and energy to produce the force of gravity.

2. How does the gravitational field differ from other fundamental forces in quantum mechanics?

The gravitational field is unique among the fundamental forces in quantum mechanics because it is the only force that has not yet been successfully described by a quantum theory. While the other three forces (electromagnetic, strong, and weak) have been unified under the Standard Model, gravity remains a challenge to incorporate into this framework.

3. How does quantum mechanics explain the behavior of gravity at the subatomic level?

In quantum mechanics, gravity is treated as a quantum field, similar to the other fundamental forces. However, due to the extremely small scale at which gravity operates, its effects are only noticeable on a macroscopic scale. At the subatomic level, the effects of gravity are negligible and can be ignored.

4. Can quantum mechanics solve the problem of unifying gravity with the other fundamental forces?

There is currently no widely accepted theory that successfully unifies gravity with the other fundamental forces. However, many scientists believe that incorporating gravity into the framework of quantum mechanics will lead to a more complete understanding of the universe and potentially solve this problem.

5. What are some current research efforts in understanding the gravitational field in quantum mechanics?

Some current research efforts in this area include string theory, loop quantum gravity, and black hole thermodynamics. These theories attempt to describe the behavior of gravity at the quantum level and provide a framework for unifying gravity with the other fundamental forces. However, there is still much work to be done in this field.

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