Test of the time dependent Schrödinger equation with very slow neutrons

Abstract

Very slow neutrons with matter wave frequencies ⩽10¹¹ Hz offer the possibility to observe “diffraction in time”, the spreading in frequency (and velocity) die to the interaction with time varying potentials. These effects can be regarded as a test of the time dependent Schrödinger equation and of the uncertainty principle $\text{ΔE · Δt =}\text{h}\text{̵}$.

As a first step we will try to observe “diffraction in time” from a fast chopper with opening times (and repetition times) of about 2(6) × 10⁻⁸s. The spreading in travel time will be observed by a new high resolution time of flight spectrometer for 30 Å neutrons, which is currently under construction. With the nominal relative energy resolution of about 8 × 10⁻⁴ we expect interferences in time from successive openings of the chopper. This can be regarded as the double slit experiment in time. In a later version it seems possible to achieve chopper frequencies close to matter wave frequencies of 200 Å neutrons.