Abstract
We study the sextic and decatic potentials energy including the odd power terms, and explore possible polynomial solutions for Schrödinger equation. Moreover, we proved that generals sextic and decatic potentials are exactly solvable under certain conditions on the potential’s parameters; these conditions connect the potential’s parameters to each other and to wave function’s zeros. We compare achieved results with those evaluated by numerical methods. Finally, we derive general expressions of the energy levels and evaluate the first eigenstates for both potentials.