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

Valentin Ioan Remus Niculescu, Diana Rodica Constantin

Publication date: 3 April 2018

Abstract: 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".

Mathematics Subject Classification ID

Ordinary differential equations (34-XX) Potential theory (31-XX) Quantum theory (81-XX) Integral transforms, operational calculus (44-XX)

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