The basic scaling method

We are interested in finding eigenstates of a -dimensional billiard whose
domain has
`volume' and whose boundary has `surface area' .
Therefore the typical system size is
.
The scaling method will find all the states in a
range
around a given wavenumber , using a *single*
diagonalization of the same numerical effort required for *each*
evaluation in the previous chapter.
Up to states of useful accuracy are returned per diagonalization,
making the method many orders of magnitude faster than any other method
known at this time.

- Tension matrix in a scaling eigenfunction basis
- Quasi-orthogonality on the boundary
- Semiclassical estimate of off-diagonal strength of
- Relation to strength estimate of Vergini and Saraceno

- Representation in a Helmholtz basis

- Solving for the scaling eigenfunctions

Alex Barnett 2001-10-03