Abstract
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum group $SU(2)_q$ as a particular case. In this deformation Planck's constant becomes an operator whose eigenvalues approach $\hbar $ for small values of $n$ (the eigenvalue of the number operator), and zero for large values of $n$ (the system is classicalized).
Highlights
There are different motivations to consider a deformation of the classical-quantum transition [1,2,3,4,5,6,7,8,9,10,11,12]
In order to identify a deformation of the classicalquantum transition from the deformed ladder operator commutation relations, we need to reformulate a classical system in terms of complex variables αi which will become the ladder operators in the quantum theory [50]
We have presented in this work a proposal for the deformation of the ladder operators associated with the Heisenberg algebra of a quantum mechanical system
Summary
There are different motivations to consider a deformation of the classical-quantum transition [1,2,3,4,5,6,7,8,9,10,11,12]. We end the list of motivations for a deformation of the classical-quantum transition pointing out the possibility that it provides a new way to try to overcome the difficulties to understand some surprising quantum mechanical effects like the phenomenon of high temperature superconductivity and Bose-Einstein condensation. In order to develop the idea, a deformation of the ladder operators algebra is proposed and contains a limit to SUð2Þq as a symmetry group In this deformation the Planck constant becomes an operator whose eigenvalues approach ħ for small values of the quantum number n, but for large values of n, the eigenvalues approach zero and the system is classicalized.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
