|
Recent Volumes |
|
Volume 1, 1998 |
|
Volume 2, 1999 |
|
Volume 3, 2000 |
|
Volume 4, 2002 |
|
Volume 5, 2002 |
|
Volume 6, 2003 |
|
Volume 7, 2004 |
|
Volume 8, 2006 |
|
Volume 9, 2006 |
|
Volume 10, 2007 |
|
Volume 11, 2007 |
|
Volume 12, 2007 |
|
Volume 13, 2008 |
|
Volume 14, 2008 |
|
Volume 15, 2008 |
|
Volume 16, 2009 |
|
Volume 17, 2011 |
|
Volume 18, 2012 |
|
|
|
Hamiltonian and quantum mechanics
Anatol Odzijewicz
|
|
Geometry & Topology Monographs 17
(2011) 385–472
|
Abstract
|
|
In these notes we review the foundations of Banach–Poisson geometry and explain
how in this framework one obtains a unified approach to the Hamiltonian and the
quantum mechanical description of the physical systems. Our considerations
will be based on the notion of Banach Lie–Poisson space and the notion of
the coherent state map, which appear to be the crucial instrument for the
clarifying what is the quantization of the classical physical (Hamiltonian)
system.
|
Keywords
Hamiltonians, quantum mechanics
|
Mathematical Subject Classification
Primary: 37K05, 53D50, 70H06, 81S10
Secondary: 34A26, 37J05, 53D17, 53D20,
81S40
|
Publication
Received: 18 May 2010
Accepted: 19 May 2010
Published: 20 April 2011
|
|
