New Appr~oach to Calculate Bound State Eigenvalues

A method of solving the radial schrgdinger equat ion for bound states is discussed. The method is based on a new piecewise represen- tation of the second derivative operator on a set of funct ions that obey the boundary conditions. This representation is trivially diago- nalised and leads to closed form expressions of the t ype En = = ~(ab + b + c/n + ...) for the eigenvalues. Examples are given forthe power-law and logarithmic potentials.