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?
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1$\begingroup$ Quantum gravity isn’t trying to quantise the Newtonian potential. The naive approach which requires a UV completion is to quantise general relativity in the same manner as a quantum field theory. $\endgroup$– JamalSDec 14, 2017 at 9:29
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$\begingroup$ Related: physics.stackexchange.com/q/387/2451 and links therein. $\endgroup$– Qmechanic ♦Dec 14, 2017 at 9:37
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$\begingroup$ To reopen this question (v1), consider to align title and main body. They seem to ask two different things. $\endgroup$– Qmechanic ♦Dec 14, 2017 at 9:42
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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.
