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Direct Measurement of the Wavefunction


Central to quantum theory, the wavefunction is a complex distribution associated with a quantum system. Despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition. Rather, physicists come to a working understanding of it through its use to calculate physical predictions about the system through the Born Rule. Inversion of these predictions is the basis of an indirect method, tomography, which is typically used to reconstruct the wavefunction. In contrast, I present a method to directly measure the wavefunction so that its real and imaginary components appear on our measurement apparatus. In an experiment, we make a weak measurement (i.e. minimally disturbing) of the transverse position of a photon. The average result of this measurement, in the subset of photons found to subsequently have zero transverse momentum, is directly proportional to the photon's transverse position wavefunction, including the phase. This method gives the wavefunction a plain and general meaning in terms of operations in the lab.