What question did this study set out to answer?

To obtain the transmission coefficient for quantum tunnelling through multiple potential barriers using the Laplace transform.

February 24, 20260 citationsOpen Access

Quantum tunnelling for thousands potential barriers

DODomenico OricchioLeonardo (United States)

Key Points

To obtain the transmission coefficient for quantum tunnelling through multiple potential barriers using the Laplace transform.
Utilized the Laplace transform for solving transmission coefficients.
Examined multiple models of potential barriers corresponding to various physical phenomena.
Applied the solution to different contexts, including electronics and nuclear physics.
Presented a new exact solution to the Schrödinger equation for tunnelling.
Identified applications in resonant-tunnelling diodes and neutron/proton diffusion.
Clarified potential uses in nuclear fission, fusion, and chemical reactions.

Abstract

I use the Laplace transform to obtain the transmission coefficient for each number of potential barriers.There are a little number of close-form solution of Schröginger equation, and this is another exact solution.It is possible to obtain the tunnelling for electronic components (resonant-tunnelling diode), or neutronand proton diffusion in astrophysics (stellar nucleosyntheis) and nuclear physics (nuclear fission and fusion),or chemical tunnelling for two molecules reaction (that I solve in a generic case), or to obtain a quantumfilter for the energy spectrum (that I solve for some coating layers).

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