We discuss the interference patterns of gravitational and whispering gallery quantum states that can be observed with neutrons, atoms, antiatoms, muonium (Mu), positronium (Ps), and other light neutral particles. A gravitational shift of interference patterns of neutron gravitational and whispering-gallery states can be easily observed with cold, very cold, or ultracold neutrons. The developed methods can be used for observing/searching for other shifts in fundamental neutron physics experiments, for instance, for measuring the gravitational constant or constraining the neutron electric charge. A series of such measurements will be made with neutrons at the PF1B, PF2, D17 facilities at the ILL. A peculiar feature of analogous atomic (anti-atomic) experiments is the much smaller effective critical energies of the materials of mirrors for (anti)atoms. We evaluated parameters that make a measurement of the hydrogen and antihydrogen whispering-gallery states and their gravitational shifts feasible. A series of such measurements will be made with hydrogen and deuterium atoms by the GRASIAN collaboration in Vienna and Turku. A similar measurement with antihydrogen atoms may be of interest for the GBAR experiment, the ASACUSA experiment, which is producing a beam of slow antihydrogen atoms, and other experiments at CERN that study the gravitational properties of antimatter. Quantum reflection (QR) of Mu and Ps from material surfaces opens the possibility of observing whispering-gallery states, although such measurements remain experimentally challenging. Because of the small masses of Mu and Ps, their effective critical energies of the mirror materials are much higher for them than the effective critical energies for hydrogen and other atoms. The observation of gravitational shifts of such states is particularly demanding because of the extremely short lifetimes of these systems. Measurements of whispering gallery states with all these atoms and particles yield precise and detailed information on the QR properties of materials, providing valuable input for both fundamental physics and surface physics studies.