  We adapt the semiclassical technique, as used in the context of instanton
transitions in quantum field theory, to the description of tunneling
transmissions at finite energies through potential barriers by complex quantum
mechanical systems. Even for systems initially in their ground state, not
generally describable in semiclassical terms, the transmission probability has
a semiclassical (exponential) form. The calculation of the tunneling exponent
uses analytic continuation of degrees of freedom into a complex phase space as
well as analytic continuation of the classical equations of motion into the
complex time plane. We test this semiclassical technique by comparing its
results with those of a computational investigation of the full quantum
mechanical system, finding excellent agreement.
