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.