1. The problem statement, all variables and given/known data i want to find a pure geometric interpretation of wave function in quantum mechanics 2. Relevant equations i want to solve schrodinger's equation as a second order partial differential equation with a pure mathmatic way to find its geometric analogous 3. The attempt at a solution when we solve the second order PDE we can find a monge cone in its space indicating the geometric objects which the solotion of the PDE equation touch it in the PDE's space so if we solve the schrodinger's equation i think we can find its geometrical anlogous. so help me please,is this imagination is correct.