Use of quantum self-friction potentials and forces in standard convention for study of harmonic oscillator

In this paper, the physical nature of quantum usual and self-friction (SF) harmonic oscillators is presented. The procedure for studying these harmonic oscillators is identical; therefore, we can benefit from the theory of the usual harmonic oscillator. To study the SF harmonic oscillator, using analytical formulae for the L(pl*)-SF Laguerre polynomials (L(p(l)*)-SFLPs) and L(alpha*)-modified SFLPs (L(alpha*)-MSFLPs) in standard convention, the V(p(l)*)-SF potentials (V(p(l)*)-SFPs), V(alpha*)-modified SFPs (V(alpha*)-MSFPs), F(p(l)*)-SF forces (F(p(l)*)-SFFs) and F(alpha*)-modified SFFs (F(alpha*)-MSFFs) are investigated, where p(l)*=2l+2-alpha* and alpha* is the integer (alpha*=alpha, -infinity<= 2) or non-integer (alpha*not equal alpha, -infinity<3) SF quantum number. We note that the potentials (V(p?l)-SFPs and V(??)-MSFPs), and forces (F(p?l)-SFFs and F(??)-MSFFs), respectively, are independent functions. It is shown that the numerical values of these independent functions are the same, i.e., V(p(l)*)num=V-num((pl)*()) and F-num((pl)*)=F-num(p(l)*). The dependence of the SF harmonic oscillator as a function of the distance is analyzed. The presented relationships are valid for arbitrary values of parameters.