Exact solutions of Schrödinger equation for the Makarov potential

We present exact solutions of Schrödinger equation with the Makarov potential using the partial-wave method for scattering states. The normalized radial wave functions of scattering states on the “k/2πk/2π scale” are expressed in terms of confluent hypergeometric functions. Equations for the determination of phase shifts and analytical properties of the scattering amplitude are discussed. The eigenvalues and normalized radial wave functions of bound states are also given.