Up to now tunneling rates in bound systems have been obtained primarily by semiclassical or wave packet calculations. A new accurate quantum timehyphen;independent method is presented. Those irregular eigenfunctions of bound systems which diverge asymptotically, but upon complex scaling of coordinatesXrarr;Xthinsp;exp(iTHgr;) become square integrable functions and are associated with complex eigenvalues are found to describe barrier penetration processes. The imaginary part of each of the complex eigenvalues of the complex scaled Hamiltonian contains the tunneling decay rate provided that the Balslevndash;Combes rotation angle is large enough. The appearance of a critical value THgr;cas the rotational angle THgr; is varied, at which a sharp transition from a real energy spectrum of the bound system to a complex eigenvalue spectrum is an indication of an exponential decay through the potential barrier. Tunneling in multiple barrier problems is important in several areas of physics and chemistry, including isomerization reactions, Josephson junction superconductors, electron tunneling from a 1Dmetallic lattice under the influence of a uniform electric field (field emission), and tunneling in theEFthinsp;1Sgr;gstate of molecular hydrogen. Several representative numerical examples are presented.
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