A transformation approach for finding first integrals of motion of dynamical systems

1974 ◽  
Vol 9 (4) ◽  
pp. 241-250 ◽  
Author(s):  
Marcelo R.M.Crespo Da Silva
Keyword(s):  
Dynamical Systems ◽  
First Integrals ◽  
Integrals Of Motion ◽  
Transformation Approach

q-Equivalent Hamiltonian Operators

1972 ◽  
Vol 50 (17) ◽  
pp. 2037-2047 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Quantum Mechanics ◽  
Classical Limit ◽  
First Integral ◽  
Canonical Commutation Relation ◽  
Equation Of Motion ◽  
First Integrals ◽  
Position Operator ◽  
Integrals Of Motion ◽  
Adjoint Operators ◽  
Hamiltonian Operators

From the equation of motion and the canonical commutation relation for the position of a particle and its conjugate momentum, different first integrals of motion can be constructed. In addition to the proper Hamiltonian, there are other operators that can be considered as the generators of motion for the position operator (q-equivalent Hamiltonians). All of these operators have the same classical limit for the probability density of the coordinate of the particle, and many of them are symmetric and self-adjoint operators or have self-adjoint extensions. However, they do not satisfy the Heisenberg rule of quantization, and lead to incorrect commutation relations for velocity and position operators. Therefore, it is concluded that the energy first integral and the potential, rather than the equation of motion and the force law, are the physically significant operators in quantum mechanics.

Symmetries, first integrals and splittability of dynamical systems

1978 ◽  
Vol 21 (7) ◽  
pp. 253-257 ◽  
Author(s):  
F. González-Gascón ◽  
F. Moreno-Insertis
Keyword(s):  
Dynamical Systems ◽  
First Integrals
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