Polynomial supersymmetry and dynamical symmetries in quantum mechanics

1995 ◽  
Vol 104 (3) ◽  
pp. 1129-1140 ◽  
Author(s):  
A. A. Andrianov ◽  
M. V. Ioffe ◽  
D. N. Nishnianidze
Keyword(s):  
Quantum Mechanics ◽  
Dynamical Symmetries

scholarly journals Differential representations of dynamical oscillator symmetries in discrete Hilbert space

2000 ◽  
Vol 5 (2) ◽  
pp. 97-106
Author(s):  
Andreas Ruffing
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Discrete Spectrum ◽  
Classical Limit ◽  
Heisenberg Algebra ◽  
Space Structure ◽  
Hermite Functions ◽  
Dynamical Symmetries ◽  
Creation And Annihilation Operators

As a very important example for dynamical symmetries in the context ofq-generalized quantum mechanics the algebraaa†−q−2a†a=1is investigated. It represents the oscillator symmetrySUq(1,1)and is regarded as a commutation phenomenon of theq-Heisenberg algebra which provides a discrete spectrum of momentum and space,i.e., a discrete Hilbert space structure. Generalizedq-Hermite functions and systems of creation and annihilation operators are derived. The classical limitq→1is investigated. Finally theSUq(1,1)algebra is represented by the dynamical variables of theq-Heisenberg algebra.

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