Volume 17 (2011)

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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

References
Publication

Received: 18 May 2010
Accepted: 19 May 2010
Published: 20 April 2011

Authors
Anatol Odzijewicz
Institute of Mathematics
University of Białystok
Akademicka 2
15-267 Białystok
Poland