On the Time-Dependent Analysis of Gamow Decay

Details On the Time-Dependent Analysis of Gamow Decay On the Time-Dependent Analysis of Gamow Decay

2009-09-17

arxiv.org/abs/0909.3251v1

Physics

Mathematical Physics

45 pages, 4 figures, Diploma thesis

Scientific paper

Gamow's approach to exponential decay of meta-stable particles via complex 'eigenvalues' (resonances) of a Hamiltonian is scrutinized. We explain the sense in which the non-square-integrable 'eigenfunctions' that belong to these resonances (Gamow functions) are relevant for the time-evolution of square-integrable wave functions. For concreteness we study a one dimensional square-well potential with a trapping region K and the evolution of wave functions, whose support is initially inside of K. It is shown that the sum over the first few time-evolved Gamow functions restricted to K yields an approximation for the evolution of these initial wave functions within the trapping region. The approximation is good for all times for which exponential decay prevails.

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