Quantum Tunneling in Deformed Quantum Mechanics with Minimal Length

Xiaobo Guo,Jun Tao,Peng Wang,Bochen Lv

doi:10.1155/2016/4502312

Abstract

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 tunneling rates through potential barriers under the WKB approximation. Finally, the minimal length effects on two examples of quantum tunneling in nuclear and atomic physics are discussed.

Highlights

Various theories of quantum gravity, such as string theory, loop quantum gravity, and quantum geometry, predict the existence of a minimal length [1,2,3]
The Generalized Uncertainty Principle (GUP) correction to the α-decay has been considered in [22]. We both find that the effects of the GUP would increase the tunneling probability and decrease the lifetime τ
We considered quantum tunneling in the deformed quantum mechanics with a minimal length

Summary

Introduction

Various theories of quantum gravity, such as string theory, loop quantum gravity, and quantum geometry, predict the existence of a minimal length [1,2,3]. Where β = β0lp2/ħ2 = β0/c2mp2l, mpl is the Planck mass, lp is the Planck length, and β0 is a dimensionless parameter With this modified commutation relation, one can find. The remaining ones are called “runaway” solutions, which are not physical and should be discarded [17, 18] They used the WKB approximation to show that the solution to the deformed Schrodinger equation: P2 ( ħ d ) ψ (x) + 2m [V (x) − E] ψ (x) = 0, i dx (10). We continue to consider other WKB connection formulas and calculate tunneling rates through potential barriers.

Tunneling through Potential Barriers

Examples

Conclusions