Physics – Quantum Physics
Scientific paper
2004-07-13
Physics
Quantum Physics
Plain TeX, 19 pages
Scientific paper
10.1016/j.physleta.2004.09.065
The scattering theory of Lax and Phillips, originally developed to describe resonances associated with classical wave equations, has been recently extended to apply as well to the case of the Schroedinger equation in the case that the wave operators for the corresponding Lax-Phillips theory exist. It is known that the bound state levels of an atom become resonances (spectral enhancements) in the continuum in the presence of an electric field (in all space) in the quantum mechanical Hilbert space. Such resonances appear as states in the extended Lax-Phillips Hilbert space. We show that for a simple version of the Stark effect, these states can be explicitly computed, and exhibit the (necessarily) semigroup property of decay in time. The widths and location of the resonances are those given by the poles of the resolvent of the standard quantum mechanical form.
Ari Tamar Ben
Horwitz Lawrence P.
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