Treatment of the quasi-harmonic potential with the centrifugal type term in the Schroedinger equation via Laplace transform

Autor:	Constantin, D. R., Niculescu, V. I. R.
Rok vydání:	2018
Předmět:	Quantum Physics Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	In the quantum frame, for 3-dimensional space, in the two body problem case, we approach the Schr\"odinger equation (SE) taking in account the potential: Vq(r)=Dr^2+(A/r)+(B/r^2) called by us quasi-harmonic potential with the centrifugal type term, with D,A,B >0 and D<<1. We use Laplace transform method (LTM) and we find for the first time an analytic solution of the Vq-potential problem. Namely, using directly and inverse Laplace transformations, we obtain the complete forms of the energy eigenvalues and wave functions. Furthermore, for this potential Vq, we make considerations about critical orbital quantum value "lc" and we obtain a useful approximation of upper bound "lc+" to "lc". Comment: 9 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1804.02455 Zobrazit plný text záznamu View this record from Arxiv