caa a22 4500 46788739X CHVBK 20180406152738.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s10714-006-0257-6 doi (NATIONALLICENCE)springer-10.1007/s10714-006-0257-6 Corichi Alejandro Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. Postal 70-543, 04510, México, D.F., México aut Quantum superposition principle and geometry [Elektronische Daten] [Alejandro Corichi] Within the Geometrical Formulation of Quantum Mechanics, quantum states are rays in the standard Hilbert space of the theory. The resulting formulation is very elegant from the geometrical viewpoint, since it allows to cast the main postulates of the theory in terms of two geometric structures, namely a symplectic structure and a Riemannian metric. However, the superposition principle of quantum mechanics is not naturally incorporated, since the quantum state space is non-linear. In this note we offer some steps to incorporate the superposition principle within the geometric description. In this respect, we argue that it is necessary to make the distinction between a projective superposition principle and a decomposition principle that should replace the standard superposition principle. We illustrate our proposal with two very well known examples, namely the spin 1/2 system and the two slit experiment, where the distinction is clear. Springer-Verlag, 2006 Hilbert space nationallicence Quantum state nationallicence Superposition principle nationallicence General Relativity and Gravitation Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 38/4(2006-04-01), 677-687 0001-7701 38:4<677 2006 38 10714 https://doi.org/10.1007/s10714-006-0257-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-006-0257-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Corichi Alejandro Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. Postal 70-543, 04510, México, D.F., México aut NATIONALLICENCE 773 0- General Relativity and Gravitation Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 38/4(2006-04-01), 677-687 0001-7701 38:4<677 2006 38 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer