Abstract
It is ironic that experimentally time is the most accurately measured physical quantity, while in quantum mechanics one must struggle to provide a definition of so practical a concept as time of arrival. Historically, one of the first temporal quantities analyzed in quantum mechanics was lifetime, a property of an unstable state. The theory of this quantity is satisfactory in two ways. First, with only the smallest of white lies, one predicts exponential decay, and generally this is what one sees. Second, at the quantitative level, one finds good agreement with a simply derived formula, the Fermi-Dirac Golden rule, Γ = 2π/ħρ(E)|〈f|H|i|2. (4.1) Equation (4.1) uses standard notation. Γ is the transition rate from an initial (unstable) state |i〉 to a final state |f〉. The transition occurs by means of a Hamiltonian H. The density of (final) states is ρ, evaluated at the (common) energy of the states |i〉 and |f〉. In terms of Γ, the lifetime is τL = 1/Γ
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Schulman, L.S. (2002). Jump Time and Passage Time: The Duration of a Quantum Transition. In: Muga, J.G., Mayato, R.S., Egusquiza, I.L. (eds) Time in Quantum Mechanics. Lecture Notes in Physics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45846-8_4
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