Effects of the Generalized Uncertainty Principle on Quantum Tunneling

TL;DR

This paper investigates how the generalized uncertainty principle (GUP), a quantum gravity concept, affects tunneling probabilities in simple quantum systems, showing that GUP increases tunneling likelihood in various models.

Contribution

It derives GUP corrections to tunneling probabilities in accessible undergraduate quantum systems using the WKB approximation, expanding prior work on GUP effects.

Findings

GUP increases tunneling probabilities in studied models

Corrections are derived for systems like alpha decay and quantum cosmogenesis

Applicable to undergraduate-level quantum mechanics education

Abstract

In a previous paper [Blado G, Owens C, and Meyers V 2014 Quantum Wells and the Generalized Uncertainty Principle Eur. J. Phys. 35 065011], we showed that quantum gravity effects can be discussed with only a background in non-relativistic quantum mechanics at the undergraduate level by looking at the effect of the generalized uncertainty principle (GUP) on the finite and infinite square wells. In this paper, we derive the GUP corrections to the tunneling probability of simple quantum mechanical systems which are accessible to undergraduates (alpha decay, simple models of quantum cosmogenesis and gravitational tunneling radiation) and which employ the WKB approximation, a topic discussed in undergraduate quantum mechanics classes. It is shown that the GUP correction increases the tunneling probability in each of the examples discussed.