We present an alternative formulation of quantum mechanics in which no reference is made to any potential function. In this formalism, the wavefunction is written as a bounded infinite sum in a complete and suitable basis with orthogonal polynomials in the energy as expansion coefficients. The asymptotics of these polynomials give the scattering phase shift, bound states and resonances for the corresponding physical system. In addition to the well-known quantum systems, this formulation enables one to obtain analytic realization of previously untreated problems.