While the TISE does represent a significant simplification over the
full-blown TDSE, the TISE is itself a formidable equation. We have
paid a price in the elimination in the time dependence from the
equation describing 
. That price is the introduction of
the unknown parameters 
, the allowed ``eigenenergies'' of the
system. While before we had a partial differential equation with an
extra variable t, at least we knew at the start the values of all of
the constants appearing in the TDSE (1). This is no
longer the case with the TISE. We must somehow determine the values
. Before discussing methods for determining the allowed 
and finding the solutions of the TISE, we will now discuss what we may
say in general about these solutions. The first two facts we will
discuss are general mathematical properties of the 
the 
respectively. The second second two facts are more physical and give
us insight into the allowed energies of a system, the 
.