Wavepackets representation conditions

The boundary conditions can also have a decisive influence on the type of representation. A first example is given by the transmitted wave at a vacuum boundary, as discussed in Section VI.B. Here the incident and reflected plane waves can be matched at the interface by a plane transmitted wave, but hardly by a transmitted beam of axisymmetric photon wavepackets. 

Each rotational state is coupled to all other states through the potential matrix V defined in (3.22). Initial conditions Xj(I 0) are obtained by expanding — in analogy to (3.26) — the ground-state wavefunction multiplied by the transition dipole function in terms of the Yjo- The total of all one-dimensional wavepackets Xj (R t) forms an R- and i-dependent vector x whose propagation in space and time follows as described before for the two-dimensional wavepacket, with the exception that multiplication by the potential is replaced by a matrix multiplication Vx-The close-coupling equations become computationally more convenient if one makes an additional transformation to the so-called discrete variable representation (Bacic and Light 1986). The autocorrelation function is simply calculated from... 

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