Ermakov-Lewis dynamic invariants with some applications

Abstract

Contents: Introduction(3).The method of Ermakov(4).The method of Milne(7). Pinney&#39;s result(8).Lewis&#39; results(8). The interpretation of Eliezer and Gray(14). The connection of the Ermakov invariant with Nöther&#39;s theorem(17). Possible generalizations of Ermakov&#39;s method(20). Geometrical angles and phases in Ermakov&#39;s problem(22). Application to the minisuperspace cosmology(26). Application to physical optics(42).Conclusions(47). Appendix A: Calculation of the integral of I(48). Appendix B: Calculation of <\hat{H}> in eigenstates of \hat{I}(49).References(50).