scholarly journals Basic hypergeometric functions and orthogonal Laurent polynomials

2012 ◽  
Vol 140 (6) ◽  
pp. 2075-2089 ◽  
Author(s):  
Marisa S. Costa ◽  
Eduardo Godoy ◽  
Regina L. Lamblém ◽  
A. Sri Ranga
Keyword(s):  
Hypergeometric Functions ◽  
Laurent Polynomials ◽  
Orthogonal Laurent Polynomials ◽  
Basic Hypergeometric Functions

QUANTUM DEFORMATIONS OF QUANTUM MECHANICS

1993 ◽  
Vol 08 (01) ◽  
pp. 89-96 ◽  
Author(s):  
MARCELO R. UBRIACO
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Time Evolution ◽  
Function Space ◽  
Scalar Product ◽  
Hypergeometric Functions ◽  
Quantum Mechanical ◽  
Basic Hypergeometric Functions ◽  
Quantum Deformations ◽  
The One

Based on a deformation of the quantum mechanical phase space we study q-deformations of quantum mechanics for qk=1 and 0<q<1. After defining a q-analog of the scalar product on the function space we discuss and compare the time evolution of operators in both cases. A formulation of quantum mechanics for qk=1 is given and the dynamics for the free Hamiltonian is studied. For 0<q<1 we develop a deformation of quantum mechanics and the cases of the free Hamiltonian and the one with a x2-potential are solved in terms of basic hypergeometric functions.

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