Evolution Operator and Projectors to Its Eigenspaces

  • Sergey LebleEmail author
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 109)


In this chapter we sketch the basic mathematical notions of dynamical projection  used in this book, starting from general relations and illustrating them by the simplest examples, following [1, 2, 3] and paying particular attention to the impact of inhomogeneities  and accompanying effects. As mentioned in the introduction [see ( 1.1)], in the waveguide propagation, after expanding all the fields in series over the transverse coordinate basis, the coefficients \(\psi _k\) of the expansions will depend on the unique longitudinal space coordinate, say x, and time. Let \(\partial ={\partial }/{\partial x}\) denote the space derivative.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Immanuel Kant Baltic Federal UniversityKaliningradRussia

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