Realisation of Snyder operators in quantum mechanics

The lack of experimental results of theories concerning the ultimate space/space–time structure, leads one to think about some simple experiments that can help demonstrate the main prediction: Space–time is discrete. In this paper, an implementation of Snyder operators is applied to simple geometries, to demonstrate that the spectrum of the position operator, in standard quantum mechanics (QM), is discrete when a parameter measuring the non-commutativity of quantum operators is introduced. The geometries are specially suitable for experiments in search of the behaviour of ultracold neutrons falling in the Earth’s gravitational potential.