Related papers: Some Studies on the Effect of Size on Various Semi…
Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle…
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…
It was found recently that tunneling probabilities over a barrier is roughly twice as large as that given by standard WKB formula. Here we explained how this come from and showed that WKB method does give a good approximation over almost…
The tunneling effect is the most popular phenomenon of quantum physics and is present in modern physical theories. Still, the most important features of this effect are already present in toy models - low dimensional quantum mechanics with…
A simple model is considered to study the effects of finite size and internal structure in the tunneling of bound two-body systems through a potential barrier. It is demonstrated that these effects are able to increase the tunneling…
In this paper we revisit the one-dimensional tunneling problem. We consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical…
The phenomenon of quantum tunneling is reviewed and an overview of applying approximate methods for studying this effect is given. An approach to a time-dependent formalism is proposed in one dimension and generalized to higher dimensions.…
Quantum tunneling across multiple barriers as yet is an unsolved problem for barrier numbers greater than five. The complexity of the mathematical analysis even for small number of barriers pushed it into the realms of Numerical Analysis.…
In the deformed quantum mechanics with a minimal length, one WKB connection formula through a turning point is derived. We then use it to calculate tunnelling rates through potential barriers under the WKB approximation. Finally, the…
A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the…
The accuracy of the WKB approximation when predicting the energy splitting of bound states in a double well potential is the main subject of this paper. The splitting of almost degenerate energy levels below the top of the barrier results…
The WKB approximation is a standard tool for studying tunnelling problems in quantum cosmology. We compare this method to the Supersymmetric WKB (SWKB) applied to a closed FRW minisuperspace model. We consider the transition from a dust…
We present an improved Wentzel-Kramers-Brillouin (WKB) calculation of tunnel splitting in one dimensional asymmetric double well potentials. We show that the tunnel splitting in general can have linear dependence on the bias energy, beside…
The tunneling probability for a system modelling macroscopic quantum tunneling is computed. We consider an open quantum system with one degree of freedom consisting of a particle trapped in a cubic potential interacting with an environment…
The complex-time method for quantum tunneling is studied. In one-dimensional quantum mechanics, we construct a reduction formula for a Green function in the number of turning points based on the WKB approximation. This formula yields a…
In this paper we discuss three methods to calculate energy splitting in cosine potential on a circle, Bloch waves, semi--classical approximation and restricted basis approach. While the Bloch wave method gives only a qualitative result,…
We adapt the semiclassical technique, as used in the context of instanton transitions in quantum field theory, to the description of tunneling transmissions at finite energies through potential barriers by complex quantum mechanical…
We study the quantum tunnel effect through a potential barrier employing a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution…
Using a method of local transmission matrix, we generalize the well-known WKB formula for a barrier penetrability to multi-channel systems. We compare the WKB penetrability with a solution of the coupled-channels equations, and show that…
Tunneling half lives are obtained in a minimalistic deformation picture of nuclear decays. As widely documented in other deformation models, one finds that the effective mass of the nucleus changes with the deformation parameter. However,…