Quantum reflection is a uniquely quantum phenomenon in which a compact object, such as a neutron or a small molecule, reflects smoothly and in a wavelike fashion from a much larger surface, such as a pool of mercury. In contrast, a classically behaving neutron or molecule will strike the same surface much like a thrown ball, hitting only at one atomic-scale location where it is either absorbed or scattered. Quantum reflection provides a powerful experimental demonstration of particle-wave duality, since it is the extended quantum wave packet of the particle, rather than the particle itself, that reflects from the larger surface. Definition Quantum reflection became an important branch of physics in the 21st century. In a workshop about quantum reflection, the following definition of quantum reflection was suggested: Quantum reflection is a classically counterintuitive phenomenon whereby the motion of particles is reverted "against the force" acting on them. This effect manifests the wave nature of particles and influences collisions of ultracold atoms and interaction of atoms with solid surfaces. Observation of quantum reflection has become possible thanks to recent advances in trapping and cooling atoms. Reflection of slow atoms Although the principles of quantum mechanics apply to any particles, usually the term "quantum reflection" means reflection of atoms from a surface of condensed matter (liquid or solid). The full potential experienced by the incident atom does become repulsive at a very small distance from the surface (of order of size of atoms). This is when the atom becomes aware of the discrete character of material. This repulsion is responsible for the classical scattering one would expect for particles incident on a surface. Such scattering is diffuse rather than specular, and so this component of the reflection is easy to distinguish. Indeed, to reduce this part of the physical process, a grazing angle of incidence is used; this enhances the quantum reflection. This requirement of small incident velocities for the particles means that the non-relativistic approximation to quantum mechanics is all that is required. Single-dimensional approximation So far, one usually considers the single-dimensional case of this phenomenon, that is when the potential has translational symmetry in two directions (say and ), such that only a single coordinate (say ) is important. In this case one can examine the specular reflection of a slow neutral atom from a solid state surface . Where one has an atom in a region of free