A Perturbative Approach to the Tunneling Phenomena
arXiv:1904.12031 · doi:10.3389/fphy.2019.00069
Abstract
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 WKB or 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 containing singular potentials (e.g., Dirac delta potentials supported by points and curves and their relativistic extensions)that it is possible to find the splitting in the bound state energies by developing some kind of perturbation method.
arXiv comment24 pages, 4 figures
References in corpus (15)
- Sinc approximation of algebraically decaying functions
- Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
- Geometrically induced spectrum in curved leaky wires
- Point interactions in a strip
- Curvature-induced bound states for a interaction supported by a curve in
- One-Dimensional Semirelativistic Hamiltonian with Multiple Dirac Delta Potentials
- Point Interaction in two and three dimensional Riemannian Manifolds
- Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the -Function Potential in 1-dimensional Relativistic Quantum Mechanics
- Statistics of wave functions for a point scatterer on the torus
- Finitely Many Dirac-Delta Interactions on Riemannian Manifolds
- Interaction of Relativistic Bosons with Localized Sources on Riemannian Surfaces
- Geometric phase related to point-interaction transport on a magnetic Lobachevsky plane
- Bound States in Models of Asymtotic Freedom
- On the Number of Bound States of Point Interactions on Hyperbolic Manifolds
- A Klein Gordon Particle Captured by Embedded Curves