We develop a geometrical approach to Schrodinger quantum mechanics, alternative to the usual one, which is based on linear and algebraic structures such as Hilbert spaces, operator algebras, etc. The starting point of this approach is the Kahler structure possessed by the set of the pure states of a quantum system. The Kahler manifold of the pure states is regarded as a "quantum phase space", conceptually analogous to the phase space of a classical hamiltonian system, and all the constituents of the conventional formulation, in particular the algebraic structure of the observables, are reproduced using a suitable "Kahler formalism". We also show that the probabilistic character of the measurement process in quantum mechanics and the uncertainty principle are contained in the geometrical structure of the quantum phase space. Finally, we obtain a characterization for quantum phase spaces which can be interpreted as a statement of uniqueness for Schrodinger quantum mechanics.

QUANTUM PHASE-SPACE FORMULATION OF SCHRODINGER MECHANICS / R. Cirelli, A. Mania, L. Pizzocchero. - In: INTERNATIONAL JOURNAL OF MODERN PHYSICS A. - ISSN 0217-751X. - 6:12(1991), pp. 2133-2146. [10.1142/S0217751X91001064]

QUANTUM PHASE-SPACE FORMULATION OF SCHRODINGER MECHANICS

L. Pizzocchero
Ultimo
1991

Abstract

We develop a geometrical approach to Schrodinger quantum mechanics, alternative to the usual one, which is based on linear and algebraic structures such as Hilbert spaces, operator algebras, etc. The starting point of this approach is the Kahler structure possessed by the set of the pure states of a quantum system. The Kahler manifold of the pure states is regarded as a "quantum phase space", conceptually analogous to the phase space of a classical hamiltonian system, and all the constituents of the conventional formulation, in particular the algebraic structure of the observables, are reproduced using a suitable "Kahler formalism". We also show that the probabilistic character of the measurement process in quantum mechanics and the uncertainty principle are contained in the geometrical structure of the quantum phase space. Finally, we obtain a characterization for quantum phase spaces which can be interpreted as a statement of uniqueness for Schrodinger quantum mechanics.
Geometric quantum mechanics ; Kahler manifolds
Settore MAT/07 - Fisica Matematica
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/189450
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 15
social impact