Question

The Schrodinger equation, the Dirac equation and the Boltzmann equation cannot be derived exactly from some more basic theory. Why then should anyone be willing to call work based on these equations scientific theories?

Answer 1

The main reason for considering these equations are the fundamental because of the fact that the theoretical predictions are an excellent match with experimental values. For example, Schrodinger equation predicts the tunneling of non-relativistic electrons and it is the basic principle of scanning electron microscopy. Similarly, one of the classic prediction of Dirac equation is the existence of positron, anti-particle of the electron. Later it is experimentally verified. Also, Boltzmann equation discusses the thermodynamic behavior of system out-of equlibrium. It widely used to understand Neutron transport and radiative transfer. These are some reasons for considering these are the fundamental equations in Physics.