A generation of exactly solvable anharmonic symmetric oscillators

Using the ideas of supersymmetric quantum mechanics, we exactly solve a con tinuous family of anharmonic potentials, which are the supersymmetric partn ers of the linear harmonic oscillators. The family includes a series of pot entials in which the excited-state energy is the same as that of the harmon ic oscillators, but the ground-state energy can be any value lower than the excited states. The shape of the potential is variable, which includes the double-well and triple-well potentials. All the potentials obtained in thi s paper are free of singularities, and the supersymmetry of the solutions i s unbroken.