ON A CONNECTION BETWEEN RADIAL SCHRODINGER-EQUATIONS FOR DIFFERENT POWER-LAW POTENTIALS

A general correspondence is given between the radial Schrödinger equations (in arbitrary dimensions) for confining- and inverse-power law potentials. The wave functions and Green's functions of the two types of potentials are shown to differ by little more than a change of variable (a special case being the well-known equivalence of the harmonic oscillator and Coulomb problems). This gives rise to relationships between the discrete state eigenvalues and matrix elements. Following the lines of a recent paper by Gazeau, the relevance of this correspondence to Sturmian representations for power law potentials is examined. Generalizations are considered for potentials containing a linear combination of powers of r. © 1980 American Institute of Physics.