Role and Scope of Dynamical Invariants in Physical Problems: Interpretation and Applications

Abstract

It is true that the invariants when defined in a broader sense play an important role in different branches of mathematics and mathematical physics, but somehow the description of physical reality limits their applications in physics and other allied sciences. In this respect while the role and the scope of the dynamical invariants for the 1D systems has been discussed at great length in the literature, it is not explored to that extent for the two and higher dimensional systems. In this chapter, we briefly highlight some possible physical interpretations known for the invariant for the TD HO system in 1D and also discuss some physical situations in different branches of mathematical sciences where not only the role of these invariants becomes transparent but also their studies may find some applications. Some possible interpretations of dynamical invariants are outlined in the next Section. In Sect. 7.2, various applications of the knowledge of these invariants are discussed. In Sect. 7.3, the role of these invariants is briefly discussed in the context of more recent topic of phases of the quantum wavefunction.