THE TRANSFORMATIVE COMPLEX ABSORBING POTENTIAL METHOD - A BRIDGE BETWEEN COMPLEX ABSORBING POTENTIALS AND SMOOTH EXTERIOR SCALING

The derivation of the transformative complex absorbing potential (TCAP ) method and its performance are discussed. This approach was develope d in a previous paper (1995 J. Phys. B: At. Mel. Opt. Phys. 28 1475) a nd illustrates the relation between complex absorbing potentials (CAPs ) and the smooth exterior scaling (SES) method. Starting from an energ y-dependent CAP one arrives at an SES-like Hamiltonian via an elementa ry similarity transformation. Developing this idea further leads to th e so-called TCAP equation. It differs from the SES Schrodinger equatio n in two respects. Firstly, the potential is not transformed and, seco ndly, an additional correction term appears. Neglecting this rather sm all term leads to a Hamilton operator that is easy to apply to time-de pendent as well as time-independent problems. This Hamiltonian can be extended order by order ending up in the full SES Hamiltonian. By nume rical application it is demonstrated that the TCAP approach is very ef ficient and can easily be generalized to the multi-dimensional case fo r which formulae are provided.