What is complete integrability in quantum mechanics

2007 ◽  
pp. 83-90 ◽  
Author(s):  
L. D. Faddeev
Keyword(s):  
Quantum Mechanics ◽  
Complete Integrability

scholarly journals TOWARDS A DEFINITION OF QUANTUM INTEGRABILITY

2009 ◽  
Vol 06 (01) ◽  
pp. 129-172 ◽  
Author(s):  
JESÚS CLEMENTE-GALLARDO ◽  
GIUSEPPE MARMO
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Degrees Of Freedom ◽  
Complete Integrability ◽  
Infinite Dimensional ◽  
Quantum Integrability ◽  
Classical Systems ◽  
Definition Of ◽  
Geometrical Formulation ◽  
Quantum Framework

We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to the quantum framework would not work because all infinite dimensional Hilbert spaces are unitarilly isomorphic and, as a consequence, it would not be easy to define degrees of freedom. We argue that a geometrical formulation of quantum mechanics might provide a way out.

The New Quantum Mechanics

2009 ◽  
Author(s):  
George Birtwistle
Keyword(s):  
Quantum Mechanics

Applied Quantum Mechanics

2006 ◽  
Author(s):  
A. F. J. Levi
Keyword(s):  
Quantum Mechanics

Quantum Mechanics

2009 ◽  
Author(s):  
Gennaro Auletta ◽  
Mauro Fortunato ◽  
Giorgio Parisi
Keyword(s):  
Quantum Mechanics

Quantum Mechanics for Nanostructures

2009 ◽  
Author(s):  
Vladimir V. Mitin ◽  
Dmitry I. Sementsov ◽  
Nizami Z. Vagidov
Keyword(s):  
Quantum Mechanics

The Logic of Quantum Mechanics

1984 ◽  
Author(s):  
Enrico G. Beltrametti ◽  
Gianni Cassinelli ◽  
Peter A. Carruthers
Keyword(s):  
Quantum Mechanics
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