A possible method for studying the properties of the neutron wave packet V.K.Ignatovich FLNP JINR Abstract The concept of the coherence length of the neutron is explored. The generally accepted definition of a Gaussian wave packet based on the method of the beam preparation, and the singular de Broglie’s wave packet are considered. Possible ways of measuring the coherence length are discussed. 1 Introduction Examination of wave packets is, apparently, the most important fundamental problem of physics today. It is clear that the wave function of the neutron is not a plane wave. It should be a vector of the Hilbert space i.e. a wave packet having certain properties. It has some size, called the coherent length, and the size can change with energy. In [1] it was reasonably noted that unstable particle with a lifetime of τ can have the size of the value of L =  ¯ hτ /m, which for the neutron is 0.75 cm. However, the finite lifetime can lead also to the definition of the packet size proportional to the neutron velocity L = vτ . So the greater the speed, the larger is the wave packet, although from a physical point of view, it seems more reasonable to consider [2], that the faster the particle, the more neutron should look like a point particle. In [3] wave packet was introduced to explain the UCN anomaly (abnormally high losses in traps). The packet size was estimated to be L ≈ 10 5 lambda Be , where λ Be is the minimal wavelength of the neutron which can be stored in beryllium traps. In this case L is the order of several millimeters, which does not contradict the assumption made in the [1]. Later [4,5] the assumption was made that the size of the wave packet depends on the speed and is proportional to the wavelength: L ≈ 10 5 λ/2π. Therefore, the thermal neutron wave packet size is up to about 10 microns. Perhaps it is correct, but how experimentally to measure the size of the wave packet — that is the question. One way is to look for neutron transmission through films at incidence at a subcritical glancing angle [4,6,7]. Some indication of the transmission was received, but there is still no certainty. More precise experiments are needed. Here another experiment is discussed. When, because of some coherent pro- cess, the neutron wave function of a polarized neutron is split into two diverging 1