AUTHOR=Erman Fatih , Turgut Osman Teoman 

TITLE=A Perturbative Approach to the Tunneling Phenomena

JOURNAL=Frontiers in Physics

VOLUME=7

YEAR=2019

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00069

DOI=10.3389/fphy.2019.00069

ISSN=2296-424X

ABSTRACT=<p>The double-well potential is a good example, where we can compute the splitting in the bound state energy of the system due to the tunneling effect with various methods, namely path-integral, WKB, and instanton calculations. All these methods are non-perturbative and there is a common belief that it is difficult to find the splitting in the energy due to the barrier penetration from a perturbative analysis. However, we will illustrate by explicit examples including singular potentials (e.g., Dirac delta potentials supported by points and curves and their relativistic extensions) it is possible to find the splitting in the bound state energies by developing some kind of perturbation method.</p>