  We combine the finite size scaling method with the meshfree spectral method
to calculate quantum critical parameters for a given Hamiltonian. The basic
idea is to expand the exact wave function in a finite exponential basis set and
extrapolate the information about system criticality from a finite basis to the
infinite basis set limit. The used exponential basis set -though chosen
intuitively- allows handling a very wide range of exponential decay rates and
calculating multiple eigenvalues simultaneously. As a benchmark system to
illustrate the combined approach, we choose the Hulthen potential. The results
show that the method is very accurate and converges faster when compared with
other basis functions. The approach is general and can be extended to examine
near threshold phenomena for atomic and molecular systems based on
even-tempered exponential and Gaussian basis functions.
