Two phenomena have been observed recently in experiments with slow neutrons: quantum states of ultracold neutrons (UCN) in the Earth’s gravitational field  and quantum states of cold neutrons (CN) in the centrifugal potential in the vicinity of a curved mirror . The first experiment presented the first observation of quantum states of matter in a gravitational field; the second one is also known as the neutron whispering gallery effect. They are related by common experimental methods used, by common mathematical description, but also by their applications in elementary particle physics, in quantum optics, in surface science . It is curious that these experiments present the first direct demonstration of the weak equivalence principle for an object in a quantum state. Much more precise measurements of/with these phenomena are going to be performed in a recently constructed second-generation GRANIT spectrometer . Analogous experiments could be probably performed in future with anti-matter atoms [5-6], with interesting applications in various domains of science.
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