  Several properties of bound states in potential $ V(x)= g^2\exp (|x|)$ are
studied. Firstly, with the emphasis on the reliability of our
arbitrary-precision construction, wave functions are considered in the two
alternative (viz., asymptotically decreasing or regular) exact Bessel-function
forms which obey the asymptotic or matching conditions, respectively. The
merits of the resulting complementary transcendental secular equation
approaches are compared and their applicability is discussed.
