The Goos-Hänchen effect is a spatial shift along an interface resulting from an interference effect that occurs for total internal reflection. This phenomenon was suggested by Sir Isaac Newton, but it was not until 1947 that the effect was experimentally observed by Goos and Hänchen. We provide the first direct, absolute, experimental determination of the Goos-Hänchen shift for a particle experiencing a potential well as required by quantum mechanics: namely, wave-particle duality. Here, the particle is a spinpolarized neutron reflecting from a film of magnetized material. We detect the effect through a subtle change in polarization of the neutron. Here, we demonstrate, through experiment and theory, that neutrons do exhibit the Goos-Hänchen effect and postulate that the associated time shift should also be observable. The longitudinal Goos-Hänchen shift is well known for photons. It was Sir Isaac Newton [1] who suggested a beam of light, specularly reflected at a glass-vacuum surface, first penetrates into the vacuum and then is attracted back toward the glass surface. The result is a shift of the incident ray over some distance along the surface of the interface as shown in Fig. 1. F. Goos and H. Hänchen were the first to observe such a shift experimentally [2,3]. Since then, this shift for electromagnetic waves have been subject of further studies [4,5], including also transverse shifts, known as the Imbert-Fedorov shift [6]. Because of the particlewave duality, as advocated by quantum mechanics, such a shift should also be observable for particles reflecting from a potential well. As a neutron possesses a magnetic moment, the neutron wave function is represented by a spinor, consisting of an up-spin wave function and a down-spin wave function. The Goos-Hänchen shift for an up-spin wave function is different from the one for a down-spin wave function due to the difference in potential well for the spin up and down wave functions. The difference in these shifts results in a different polarization after reflection from the mirror with respect to the polarization before reflection.For neutrons, experimental possibilities have been discussed [7,8] previously, but to the best of the authors' knowledge, these experiments have not been performed. The measurements described by Pleshanov [9] are indirect measurements of the shift, determining the effect on the reflectivity, similar as the ones described by Toperverg [10]. Experimentally, to observe this change in polarization requires a high neutron flux instrument with excellent control and characterization of the neutron spin polarization. The development of the spin-echo neutron reflectometer OffSpec [11,12] at ISIS second target station enables measurement of the difference in Goos-Hänchen shift via the direct and unambiguous measurement of the polarization change during reflection.The practical importance of the shift for neutrons is for the design of neutron waveguides as discussed by Rohwedder [13] similar to Pillon [14] and it can also be used to study the co...