Analysis of the spectrum generating algebra method for obtaining energy spectra

Patricio Cordero, Jamil Daboul
2005 Journal of Mathematical Physics  
We analyze and clarify how the SGA ͑spectrum generating algebra͒ method has been applied to different potentials. We emphasize that each energy level E obtained originally by Morse belongs to a different so͑2 , 1͒ multiplet. The corresponding wave functions ⌿ are eigenfuntions of the compact generators J 0 with the same eigenvalue k 0 , but with different eigenvalues q of the Casimir operators Q. We derive a general expression for all effective potentials which have ⌿ ,+m ͑r͒ ϰ ͑J + ͒ m ⌿ , ͑r͒
more » ... ϰ ͑J + ͒ m ⌿ , ͑r͒ as eigenfunctions, without using supersymmetry formalism. The different actions of SGA is further illustrated by two diagrams.
doi:10.1063/1.1895106 fatcat:7uycazwxvzcgznhkaimlzlns5q