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The problem of determining the wave function of a physical system based on the graphical representation of its zeros is considered. It can be dealt with by invoking the Bargmann representation in which the wave functions are represented by analytic functions with an appropriate definition of the scalar product. The Weierstrass factorization theorem can then be applied. Examples of states that can be guessed from the pictorial representation of zeros by both the human eye and, possibly, by machine learning systems are given. The quality of recognition by the latter has been tested using Convolutional Neural Networks.
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S. Ahmed, C. S. Muñoz, F. Nori, and A. F. Kockum. Classification and reconstruction of optical quantum states with deep neural networks. Physical Review Research, 3(3):033278, 2021. https://doi.org/10.1103/PhysRevResearch.3.033278. (Crossref)
J. C. Baez, I. E. Segal, and Z. Zhou. Introduction to Algebraic and Constructive Quantum Field Theory. Princeton University Press, 1992. (Crossref)
V. Bargmann. On a Hilbert space of analytic functions and an associated integral transform part I. Communications on Pure and Applied Mathematics, 14(3):187-214, 1961. https://doi.org/10.1002/cpa.3160140303. (Crossref)
A. J. Hanson. A construction for computer visualization of certain complex curves. Notices of the American Mathematical Society, 41(9):1156-1163, 1994.
J. Milnor. Singular points of complex hypersurfaces. Princeton University Press, 1969. (Crossref)
W. Rudin. Real and Complex Analysis. McGraw Hill, Boston, USA, 3rd edn., 1987.
I. E. Segal. Mathematical problems of relativistic physics. In: M. Kac, ed., Proc. Summer Seminar, vol. II of Lectures in Applied Mathematics. American Mathematical Society, Boulder, Colorado, USA, 1960. Chapter VI.
D. Walls and G. J. Milburn. Quantum Optics. Springer, Berlin, 2nd edn., 2008. (Crossref)
T. Xin, S. Lu, N. Cao, G. Anikeeva, D. Lu, et al. Local-measurement-based quantum state tomography via neural networks. NPJ Quantum Information, 5(1):109, 2019. https://doi.org/10.1038/s41534-019-0222-3. (Crossref)
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