Corpus ID: 237439612

Nonrelativistic Fundamental Quantum and Classical Wave Equations

  title={Nonrelativistic Fundamental Quantum and Classical Wave Equations},
  author={Zdzislaw E. Musielak},
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians exist. It is shown that the asymmetric equations are Galilean invariant but the symmetric ones are not. By specifying quantum and classical physical settings, the constants in the equations are determined and the fundamental wave equations, including the… 


Linear and nonlinear waves
The study of waves can be traced back to antiquity where philosophers, such as Pythagoras, studied the relation of pitch and length of string in musical instruments and the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt in his treatise Theory of Sound.
The Inverse Variational Problems in Classical Mechanics
  • 1999