https://doi.org/10.1140/epjp/s13360-022-03525-6
Regular Article
Analysis of quantum decay law: is quantum tunneling really exponential?
Department of Physics, Hakim Sabzevari University, P. O. Box 397, Sabzevar, Iran
c s.alavi@hsu.ac.ir, alaviag@gmail.com
Received:
5
April
2022
Accepted:
22
November
2022
Published online:
9
December
2022
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 
are analyzed. The results exhibit non-exponential behavior for survival probability at short and intermediate times.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
