Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality

Details Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality

2002-06-20

arxiv.org/abs/quant-ph/0206145v1

Phys. Rev. A 66 (2002), 012107 1-11

Physics

Quantum Physics

23 pages, no figures, accepted by Phys. Rev. A

Scientific paper

10.1103/PhysRevA.66.012107

The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of standard quantum mechanics; the Lorentzian energy distribution must be extended to the full real axis $-\infty

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