Exact solutions of the Schrodinger equation with inverse-power potential

The Sckrodinger equation for stationary states is studied in a central pote ntial V(r) proportional to r(-beta) in an arbitrary number of spatial dimen sions. The presence of a single term in the potential makes it impossible t o use previous algorithms, which only work for quasi-exactly-solvable probl ems. Nevertheless, the analysis of the stationary Schrodinger equation in t he neighbourhood of the origin and of the point at infinity is found to pro vide relevant information about the desired solutions for all values of the radial coordinate. The original eigenvalue equation is mapped into a diffe rential equation with milder singularities, and the role played by the part icular case beta = 4 is elucidated. In general, whenever the parameter beta is even and larger than 4, a recursive algorithm for the evaluation of eig enfunctions is obtained. Eventually, in the particular case of two spatial dimensions, the exact form of the ground-state wave function is obtained fo r a potential containing a finite number of inverse powers of r, with the a ssociated energy eigenvalue.