Abstract
We discuss an algebraic technique to construct the Green's function for systems described by the noncompact so(2, 1) Lie algebra. We show that this technique solves the one-dimensional linear oscillator and Coulomb potentials and also generates particular solutions for other one-dimensional potentials. Then we construct explicitly the Green's function for the three-dimensional oscillator and the three-dimensional Coulomb potential, which are generalizations of the one-dimensional cases, and the Coulomb plus an Aharonov-Bohm potential. We discuss the dynamical algebra involved in each case and also find their wave functions and bound state spectra. Finally we introduce a point canonical transformation in the generators of so(2, 1) Lie algebra, show that this procedure permits us to solve the one-dimensional Morse potential in addition to the previous cases, and construct its Green's function and find its energy spectrum and wave functions.
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.
