Physics – Quantum Physics
Scientific paper
1998-03-29
J.Phys.A31:1297-1305,1998
Physics
Quantum Physics
15 standard LaTeX 2e (11pt, A4) pages. The packages AMS-LaTeX and amsfonts are required
Scientific paper
10.1088/0305-4470/31/4/017
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is governed via (a kind of) a parallel transport in this bundle. Some problems concerning observables are considered. There are derived the equations of motion for the state sections and observables. We show that up to a constant the matrix of the coefficients of the evolution operator (transport) coincides with the matrix of the Hamiltonian of the investigated quantum system.
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