  We first review the spectrum of the Laplacian operator on a general Laakso
Space before considering modified Hamiltonians for the infinite square well,
parabola, and Coulomb potentials. Additionally, we compute the spectrum for the
Laplacian and its multiplicities when certain regions of a Laakso space are
compressed or stretched and calculate the Casimir force experienced by two
uncharged conducting plates by imposing physically relevant boundary conditions
and then analytically regularizing the result. Lastly, we derive a general
formula for the spectral zeta function and its derivative for Laakso spaces
with strict self-similar structure before listing explicit spectral values for
cases of interest.
