Mathematical problems of stochastic quantum mechanics: Harmonic analysis on phase space and quantum geometry

1986 ◽  
Vol 6 (1) ◽  
pp. 1-18 ◽  
Author(s):  
S. Twareque Ali ◽  
Eduard Prugovečki
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Harmonic Analysis ◽  
Quantum Geometry ◽  
Mathematical Problems

Invariance Groups in Classical and Quantum Mechanics

1973 ◽  
Vol 28 (3-4) ◽  
pp. 538-540 ◽  
Author(s):  
D. J. Simms
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Energy Levels ◽  
Classical Mechanics ◽  
Symmetry Groups ◽  
Casimir Invariants ◽  
Classical Phase Space ◽  
Invariance Groups ◽  
Classical And Quantum Mechanics

AbstractThis is a report on some new relations and analogies between classical mechanics and quantum mechanics which arise out of the work of Kostant and Souriau. Topics treated are i) the role of symmetry groups; ii) the notion of elementary system and the role of Casimir invariants; iii) energy levels; iv) quantisation in terms of geometric data on the classical phase space. Some applications are described.

scholarly journals Harmonic analysis on the quotient spaces of Heisenberg groups

1991 ◽  
Vol 123 ◽  
pp. 103-117 ◽  
Author(s):  
Jae-Hyun Yang
Keyword(s):  
Quantum Mechanics ◽  
Heisenberg Group ◽  
Harmonic Analysis ◽  
Unitary Representation ◽  
Lie Group ◽  
Theta Series ◽  
Foundations Of Quantum Mechanics ◽  
Nilpotent Lie Group ◽  
Heisenberg Groups ◽  
Quotient Spaces

A certain nilpotent Lie group plays an important role in the study of the foundations of quantum mechanics ([Wey]) and of the theory of theta series (see [C], [I] and [Wei]). This work shows how theta series are applied to decompose the natural unitary representation of a Heisenberg group.

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