Symmetrized exponential oscillator

Abstract

Several properties of bound states in potential V(x) = g² exp(Formula presented.)x(Formula presented.) 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.