Ermakov-Lewis dynamic invariants with some applications

Details Ermakov-Lewis dynamic invariants with some applications Ermakov-Lewis dynamic invariants with some applications

2000-02-03

arxiv.org/abs/math-ph/0002005v3

Physics

Mathematical Physics

51 pages, MS Thesis supervised by HC Rosu, several misprints corrected

Scientific paper

Contents: Introduction(3).The method of Ermakov(4).The method of Milne(7). Pinney's result(8).Lewis' results(8). The interpretation of Eliezer and Gray(14). The connection of the Ermakov invariant with N\"other's theorem(17). Possible generalizations of Ermakov's method(20). Geometrical angles and phases in Ermakov'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).

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