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I ask this because I heard that gravity is perhaps not "quantizable" but, on the other hand, schrodinger equation admits potentials like harmonic oscilator and electric (hydrogen atom). So why not do the same with gravity potential?

Samuel Díaz
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But this is exactly what is done here: https://arxiv.org/abs/hep-ph/0502081

Cold neutrons in quantized states in the (Newtonian) gravitational potential, experimentally measured.

entrop-x
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