Bonn 2025 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 63: Poster – Quantum Information (joint session QI/Q)
Q 63.22: Poster
Thursday, March 13, 2025, 17:00–19:00, Tent
What can we learn from the phase of the momentum wave function? — •André Knoll1, Leon Cohen2, and Wolfgang Schleich1 — 1Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany — 2Department of Physics, Hunter College of the City University of New York, 695 Park Ave., New York, NY 10065, United States of America
Due to the Born rule of quantum mechanics, the amplitude of the wave function is often emphasized, while the phase is frequently overlooked. However, a closer examination reveals that the phase, particularly when encoded by the Fourier transform of position space, contains critical information about the original wave function. Building on signal processing techniques introduced by Oppenheim et al. in 1981 (Proc. IEEE, 69, 5, pp. 529-541), we adapt and extend these methods to the quantum mechanical framework. In particular, we show that even when we replace the amplitude of the momentum wave function by a constant, the phase of the momentum wave function allows a partial reconstruction of the position wave function. Our findings underscore the fundamental role of the phase in Fourier-based transformations, offering new insights into quantum mechanics and potential applications in quantum information science.
Keywords: Wigner Function; Fourier-based Transformation; Phase of the Wavefunction