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Birkhäuser Basel eBooks

Relativistic Quantum Theory for Finite Time Intervals [84]

Published Jan 1, 2009• 0 citations
Publisher

Abstract

If transition probabilities are evaluated for transitions occuring during a finite time interval, additional divergencies occur different from those commonly encountered for infinite time intervals. The expressions obtained can however be made convergent, if an indeterminacy of time is attributed to each epoch of observation. The method is applied to the emission of a photon by a free electron. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/978-3-7643-8878-2_27

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If transition probabilities are evaluated for transitions occuring during a finite time interval, additional divergencies occur different from those commonly encountered for infinite time intervals. The expressions obtained can however be made convergent, if an indeterminacy of time is attributed to each epoch of observation. The method is applied to the emission of a photon by a free electron. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
When the movement of a particle with noise was introduced in Chapter I, we were interested in the source of the noise, but postponed further discussion about it, accepting that the noise is presumably caused by the structure of the vacuum itself, and also by our mathematical method of treating the problem. We now return to the subject. On the other hand, we have seen in Chapter IV that the single particle interpretation of quantum mechanics is problematic, since in exited states of an electron, say in a hydrogen atom, the ergodic decomposition occurs at the zero sets of distribution densities (see Theorems 5.2.2 and 5.4.2). In other words, since the tunnelling is not allowed at the zero sets, the long-time average of a sample path cannot realize the predicted distribution of an electron in an excited state. This indicates that quantum mechanics must be a statistical theory. To clarify this point we need an additional mathematical structure. A statistical model was discussed in chapters VII and VIII of Nagasawa (1993) to solve this problem. We will explain it briefly, and apply it to relativistic quantum particles. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
A brief description is given of how low energy electron beam scattering experiments may be conducted in the energy range down to a few meV. Experimental data demonstrating virtual state scattering in CO 2 are shown. Expressions are given for the time delays (or lifetimes) of low energy electron molecule encounters and these expressions are used to give insight into the nature of virtual state scattering. These ideas are extended to include cold atom collisions and it is shown that there is a universal maximum collision lifetime, for an ultracold collision energy E, given by (2E). 1 These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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