Two related physical phenomena have recently been observed: quantum states of ultracold neutrons in the gravitational field above a flat mirror, and quantum states of cold neutrons in an effective centrifugal potential in the vicinity of a concave mirror. The two phenomena are similar in terms of their associated experimental methods and mathematical representations as well as in terms of their applications in particle physics, quantum optics, and surface physics. It is curious that the measurement of the near-surface quantum states of these two types is the first direct demonstration of the weak equivalence principle for a massive object in a quantum state. Analogous experiments using anti-hydrogen atoms are not only feasible but also provide a tool for precision measurements of their gravitational properties.
