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Spontaneous transitions in quantum mechanics. (English) Zbl 0992.81090

Summary: The problem of spontaneous pair creation in static external fields is reconsidered. A weak version of the conjecture proposed by G. Nenciu [Commun. Math. Phys. 76, 117-280 (1980)] is stated and proved. The method reduces the proof of the general conjecture to the study of the evolution associated with the time-dependent Hamiltonian, \(H_\varepsilon(t)\), of a vector which is the eigenvector of \(H_\varepsilon(t)\) at some given time. A possible way of proving the general conjecture is discussed.

MSC:

81V10 Electromagnetic interaction; quantum electrodynamics
81U99 Quantum scattering theory
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