https://doi.org/10.1140/epjp/s13360-024-05466-8
Regular Article
A Clebsch portrait for Schrödinger’s theory
1
Dipartimento di Matematica e Applicazioni, Universitá di Milano-Bicocca, Via Cozzi 55, 20125, Milano, Italy
2
Dipartimento di Matematica “Felice Casorati”, Università degli Studi di Pavia, Via Ferrata 5, 27100, Pavia, Italy
3
Dipartimento di Matematica e Fisica “Niccolò Tartaglia”, Università Cattolica del Sacro Cuore, Via della Garzetta 48, 25133, Brescia, Italy
Received:
10
March
2024
Accepted:
16
July
2024
Published online:
7
August
2024
In this note we pursue the investigation initiated in Spera M (in: Nielsen, Barbaresco, (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, Springer, Cham, 2023) by addressing geometric and topological issues concerning the zero set of the wave function, provided it is a knot in 3-space. Since, the standard Madelung velocity breaks down thereat, it is necessary to resort to the Clebsch geometry of the probability current shown in the above paper. This leads to considering several tightly interknit symplectic manifolds.
Gabriele Barbieri and Mauro Spera have contributed equally to this work.
Contribution to the Focus Point on “Mathematics and Physics at the Quantum-Classical Interface” edited by D.I. Bondar, I. Joseph, G. Marmo, C. Tronci.
© The Author(s) 2024
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