  The Schrodinger equation has been considered to be a postulate of quantum
physics, but it is also perceived and derived heuristically as the quantum
equivalent of the classical energy relation. We indicate that the Schrodinger
equation cannot be a physical postulate, and we show that the heuristic
derivations wrongly consider that the particle kinetic energy is proportional
to the square of the momentum operator acting on the wavefunction. The correct
term is proportional to the square of the momentum. Analyzing particle
interactions, we realize that particles have multiple virtual motions and that
each motion is accompanied by a wave that has constant amplitude. Accordingly,
we define the wavefunction as the superposition of the virtual waves of the
particle. As a result, quantum mechanics becomes a local and global theory,
while in the traditional formulation it is a local theory. In several
interaction settings we can tell what particle motions arise and explain the
outcomes in simple and tangible terms. Most importantly, the mathematical
foundation of quantum mechanics becomes clear and justified, and we derive the
Schrodinger, Dirac, etc. equations as the conditions the wavefunction must
satisfy at each space-time point in order to fulfill the respective total
energy equation.
