Non-commutative Oscillators and the commutative limit
B.Muthukumar, P.Mitra
TL;DR
This paper demonstrates that non-commutative anharmonic oscillators transition smoothly to their commutative counterparts in first order perturbation theory, offering a new approach to simplify perturbation problems.
Contribution
It introduces a method where non-commutativity transforms degenerate perturbation problems into non-degenerate ones, facilitating analysis.
Findings
Anharmonic oscillators in non-commutative space behave smoothly in the commutative limit.
Non-commutativity converts degenerate perturbation problems into non-degenerate ones.
The behavior parallels that of harmonic oscillators in the commutative limit.
Abstract
It is shown in first order perturbation theory that anharmonic oscillators in non-commutative space behave smoothly in the commutative limit just as harmonic oscillators do. The non-commutativity provides a method for converting a problem in degenerate perturbation theory to a non-degenerate problem.
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