The effects of general relativistic gravity on quantum mechanics are thoroughly investigated. The Schr\"odinger equation is derived for a nonrelativistic spinless particle and for a spin-$1/2$ particle, with the general relativistic corrections of Earth's gravity up to the first post-Newtonian order, O(1/c²). The phase differences due to the post-Newtonian corrections in quantum interferometer experiments are also calculated.
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Wajima et al. (1997) studied this question.
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