The Schrödinger equation for bound state systems in the oscillator representation (Q1372479)

The aim of the paper is to calculate the spectrum \(E_{n,l}\) and wave functions \(\psi_{n,l}(z)\) of Schrödinger equation \[ \Biggl[-{1\over 2r} \Biggl({d\over dr}\Biggr)^2r+ {l(l+1)\over r^2}+ V(r)\Biggr]\psi_{n,l}(r)= E_{n,l}\psi_{n,l}(r), \] where \(V(r)\to 0\) for \(r\to\infty\) or \(V(r)\to r^{2\sigma}\) \((\sigma>0)\) for \(r\to\infty\). The method consists in the following: to change the variable \(r=r(s)\) and identify the transformed equation with a Schrödinger equation in a space with different dimensions.