Semiclassical analysis of level widths for one-dimensional potentials

Details Semiclassical analysis of level widths for one-dimensional potentials Semiclassical analysis of level widths for one-dimensional potentials

1999-10-29

arxiv.org/abs/quant-ph/9910121v1

Am. J. Phys. 69, 201-206 (2001)

Physics

Quantum Physics

8 pages, 2 figures, RevTeX

Scientific paper

10.1119/1.1288129

We present a semiclassical study of level widths for a class of one-dimensional potentials in the presence of an ohmic environment. Employing an expression for the dipole matrix element in terms of the Fourier transform of the classical path we obtain the level widths within the Golden rule approximation. It is found that for potentials with an asymptotic power-law behavior, which may in addition be limited by an infinite wall, the width that an eigenstate of the isolated system acquires due to the coupling to the environment is proportional to its quantum number.

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