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2010 | 8 | 1 | 42-48
Article title

On some hydrodynamical aspects of quantum mechanics

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EN
Abstracts
EN
In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the complex polynomial (i.e. Borel-Weil) realization of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dimensional geometric quantum mechanics, the Schrödinger velocity field on projective Hilbert space is divergence-free (being Killing with respect to the Fubini-Study metric) and fulfils the stationary Euler equation, with pressure proportional to the Hamiltonian uncertainty (squared). We explicitly determine the critical points of the pressure of this “Schrödinger fluid”, together with its vorticity, which turns out to depend on the spacings of the energy levels. These results follow from hydrodynamical properties of Killing vector fields valid in any (finite dimensional) Riemannian manifold, of possible independent interest.
Publisher

Journal
Year
Volume
8
Issue
1
Pages
42-48
Physical description
Dates
published
1 - 2 - 2010
online
15 - 11 - 2009
Contributors
author
  • Dipartimento di Informatica, Università degli Studi di Verona, Ca’ Vignal 2, Strada le Grazie 15, I-37134, Verona, Italia, mauro.spera@univr.it
References
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Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-009-0070-4
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