On the Time-Dependent Analysis of Gamow Decay
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...
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Zusammenfassung: | 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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DOI: | 10.48550/arxiv.0909.3251 |