Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 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.

20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: stat
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn