Abstract
We consider a quantum mechanical system consisting of a linear chain of harmonic oscillators coupled by a nearest neighbor interaction. The system configuration can be closed (periodic boundary conditions) or open (non-periodic case). We show that such systems can be considered as Wigner Quantum Systems (WQS), thus yielding extra solutions apart from the canonical solution. In particular, a class of WQS-solutions is given in terms of unitary representations of the Lie superalgebra gl(1|n). In order to determine physical properties of the new solutions, one needs to solve a number of interesting but dificult representation theoretical problems. We present these problems and their solution, and show how the new results yield attractive properties for the quantum system (energy spectrum, position probabilities, spacial properties).
Sign-in/Register to access full text options 
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
