  Exact solutions, in terms of special functions, of all wave equations $%
u_{xx} - u_{tt} = V(x) u(t,x)$, characterised by eight inequivalent time
independent potentials and by variable separation, have been found. The real
valueness of the solutions from computer algebra programs is not always
manifest and in this work we provide ready to use solutions. We discussed
especially the potential $\cosh^{-2}x (m_1 + m_2 \sinh x)$. Such potential
approximates the Schwarzschild black hole potential for even parity.
