Journal
EUROPEAN JOURNAL OF PHYSICS
Volume 37, Issue 2, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0143-0807/37/2/025401
Keywords
tunnelling; generalised uncertainty principle; minimal length; alpha decay; quantum cosmogenesis; WKB; gravitational tunnelling radiation
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In a previous paper (Blado et al 2014 Eur. J. Phys. 35 065011), we showed that quantum gravity effects can be discussed with only a background in nonrelativistic quantum mechanics at the undergraduate level by looking at the effect of the generalised uncertainty principle (GUP) on the finite and infinite square wells. In this paper, we derive the GUP corrections to the tunnelling probability of simple quantum mechanical systems which are accessible to undergraduates (alpha decay, simple models of quantum cosmogenesis and gravitational tunnelling radiation) and which employ the WKB approximation, a topic discussed in undergraduate quantum mechanics classes. It is shown that the GUP correction increases the tunnelling probability in each of the examples discussed.
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