Following [137], the number of
samples per wavelength I will call
.
A practical choice of
will depend on what type of wavefunction and
billiard we have, as well as the required accuracy of
.
I found is sufficient for most work involving the stadium billiard
and evanescent waves components of
or less.
In this shape, the convergence with
does not follow any obvious power-law,
but for
I found the fraction error on
is
for
wavefunctions composed of random (real) plane waves.
If highly evanescent waves are present (up to
),
needs to be slightly higher (about 10).
Certainly the
of 30 quoted by [137] is excessive,
considering the fact that their PWDM basis set only includes real plane waves.
In the scaling method, I find that
errors due to a smaller
cause spurious states
(Section 6.3.3) to enter earlier than is necessary.
However, the accuracy of the valid states found does not seem very dependent
on
.
Further study on the accurate evaluation of these integrals is necessary; in particular a way to handle corners and `kinks' which has high-order (preferably exponential) convergence is sought.