The hamiltonian is not in the wave function but only exist when the amplitude is squared. But in the book "Deep Down Things". Why is the Schrodinger Equation composed of kinetic plus potential terms equal total energy. Is it not all about probability amplitude? How can probability amplitude have kinetic or potential energy? Bruce Schumm quoted in Deep Down Things: "Finally, notice that the Schrodinger equation consists of three terms: two to the left of the equals sign (separated by the “_” sign) and one to the right of the equals sign. The first term is the mathematical representation of the procedure that, once you know y(x), tells you how to determine the kinetic energy possessed by the particle at any location x. The second term, to the right of the “_” sign, is the potential energy times the value of the wave function at the location x. The third term, to the right of the “_” sign, is the total energy times the wave function y(x). So, if we look at the factors that multiply the wave function in the Schrodinger equation, we find that to the left of the equals sign we have the sum of the kinetic plus potential energies at the point x, while to the right of the equals sign, we have the total energy. Thus, the Schrodinger equation is just the wave-mechanical statement that the sum of the kinetic and potential energies at any given point is just equal to the total energy—the Schrodinger equation is simply the quantum-mechanical version of the notion of energy conservation. From this quantum-mechanical formulation of energy conservation arises the full set of constraints that prescribe the possible quantum mechanical wave functions for the object. This again illustrates the central importance of the idea of energy conservation (note 3.11)."