Geodesic
Exponential decay law and irreversibility of decay and collision processes
Applications of Mathematics, Tome 19 (1974) no. 5, pp. 307-315

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It is assumed that any decay process is described in a Hilbert space $\Cal H=\oplus \Cal H_D$, where $\Cal H_A$ corresponds to an unstable particle and $\Cal H_D$ to its decay products. It is shown that the generalized Weisskopf-Wigner condition (which guarantees an exponential decay law of the given unstable particle) has a close relation to the irreversibility of decay processes as well as of collision ones described in the same space $\Cal H$. If unitarity is added the principal structure of $\Cal H$ is identical with that onwhich the scattering theory of Lax and Phillips is based.
It is assumed that any decay process is described in a Hilbert space $\Cal H=\oplus \Cal H_D$, where $\Cal H_A$ corresponds to an unstable particle and $\Cal H_D$ to its decay products. It is shown that the generalized Weisskopf-Wigner condition (which guarantees an exponential decay law of the given unstable particle) has a close relation to the irreversibility of decay processes as well as of collision ones described in the same space $\Cal H$. If unitarity is added the principal structure of $\Cal H$ is identical with that onwhich the scattering theory of Lax and Phillips is based.
DOI : 10.21136/AM.1974.103547
Classification : 47A40 
Alda, Václav; Kundrát, Vojtěch; Lokajíček, Miloš Václav. Exponential decay law and irreversibility of decay and collision processes. Applications of Mathematics, Tome 19 (1974) no. 5, pp. 307-315. doi: 10.21136/AM.1974.103547
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[4] Lax P., Phillips R. S.: Scattering theory. Academic Press, New York-London, 1967. | MR | Zbl

[5] Fonda L., Ghirardi G. C.: Some remarks on the origin of the deviations from the exponential decay law of an unstable particle. Nuovo Cimento (1972), 10 A, 850. | MR

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