In search of hidden symmetries

This paper exemplifies the importance of finding hidden symmetries of differential equations that are models of physical phenomena. The hidden symmetries (Lie symmetries) may be determined by either linking together different equations for certain values of their parameters or transforming the original model into another equivalent system of equations that may have more symmetries. Therefore, hidden symmetries may help to solve the original model or yield its hidden properties, e.g. linearity and conservation laws. Moreover Noether symmetries are shown to be preserved by going from classical to quantum mechanics, namely from Lagrangian systems to the corresponding time-dependent Schrödinger equation.