Semiclassical analysis of level widths for one-dimensional potentials

We present a semiclassical study of level widths for a class of one-dimensi onal potentials in the presence of an ohmic environment. Using a semiclassi cal approach for the dipole matrix element we obtain the level widths withi n the golden rule approximation. For potentials with an asymptotic power-la w behavior, which may in addition be Limited by an infinite wall, we find a universal result: The level widths are proportional to the corresponding q uantum number. (C) 2001 American Association of Physics Teachers.