The wave function is the cornerstone of quantum mechanics, although it is still open to different interpretations. It has been shown that the amplitude and the phase of a wave function are manifested in the imaginary and real parts of the momentum weak value, respectively. Based on this, we develop a weak measurement scheme to reconstruct the wave function through measuring the momentum weak value. A proof-of-principle experiment is made to confirm the feasibility of our measurement scheme, in which the polarization states and the momentum of light are coupled. We believe the experimental protocol has the potential to be applied in diverse fields such as wave-front sensing, edge detection, and optical communication, and measurement of the momentum weak value may offer valuable insight to better understand quantum mechanics.

中文翻译：

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通过动量弱值重构波函数

波函数是量子力学的基石，尽管它仍然有不同的解释。已经表明，波函数的幅度和相位分别表现为动量弱值的虚部和实部。在此基础上，我们开发了一种弱测量方案，通过测量动量弱值来重建波函数。进行了原理验证实验以确认我们的测量方案的可行性，其中偏振态和光的动量是耦合的。我们相信该实验协议具有应用于波前传感、边缘检测和光通信等不同领域的潜力，并且动量弱值的测量可能为更好地理解量子力学提供有价值的见解。