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Analysis of quantum decay law: is quantum tunneling really exponential?

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Abstract

The exponential decay law is well established since its first derivation in 1928; however, it is not exact but only an approximate description. In recent years some experimental and theoretical indications for non-exponential decay have been documented. First we solve analytically the time-dependent Schrödinger equation in one dimension for a potential consisting of an infinite wall plus a rectangular barrier with finite width and also a cut harmonic oscillator potential by considering it as a sequence of square potentials. Then using the staggered Leap-Frog method, we solve the time-dependent Schrödinger equation for the cut harmonic oscillator potential. In both methods, time dependence of the survival probability of the particle and the decay parameter \( \lambda \) are analyzed. The results exhibit non-exponential behavior for survival probability at short and intermediate times.

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Acknowledgements

We would like to express our gratitude to Francesco Giacosa for his comments to improve this manuscript. S. A. Alavi is highly delighted and thankful of INFN, Turin and specially Carlo Giunti. It was there that the initial spark of this work was ignited.

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Authors and Affiliations

  1. Department of Physics, Hakim Sabzevari University, P. O. Box 397, Sabzevar, Iran

    M. S. Hosseini-Ghalehni, B. Azadegan & S. A. Alavi

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  1. M. S. Hosseini-Ghalehni
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  2. B. Azadegan
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  3. S. A. Alavi
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Correspondence to S. A. Alavi.

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Hosseini-Ghalehni, M.S., Azadegan, B. & Alavi, S.A. Analysis of quantum decay law: is quantum tunneling really exponential?. Eur. Phys. J. Plus 137, 1326 (2022). https://doi.org/10.1140/epjp/s13360-022-03525-6

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