• Discovery of the Schrodinger equation • Derivation (uniqueness) of the Schrodinger equation • High order equation of the Schrodinger type • Nonlocal symmetry of the Schrodinger equation [2, 7] • High-order evolution equations. Dependence of mass on velocity in the nonlocal Galilei-invariant theory [6, 19] • Galilei relativity principle and nonlinear Schrodinger-type equations [2, 5, 10–17] • Nonlocal symmetry of the linear Schrodinger–de Broglie–Klein–Gordon–Fock– Kudar–de Donder–Van Dunger [3, 18, 8] • Nonlocal Galilei symmetry of a relativistic equation [8, 9] • Nonlocal Galilei symmetry of the Dirac equation [7] • Galilei symmetry of a relativistic equation.
An algorithm is proposed for research into the symmetrical properties of theoretical and mathematical physics equations. The application of this algorithm to the free Schrodinger equation permited us to establish that in addition to the known Galilei symmetry, the free Schrodinger equation possesses also the relativistic symmetry in some generalized sense. This property of the free Schrodinger equation permits the equation to be extended into the relativistic area of movements of a particle being studied.