On quantum traversability of wormholes

Abstract

In this paper we study the possibility of non-relativistic quantum particles to traverse the generalized Ellis-Bronnikov wormholes by considering quantum effects, such as tunneling. We have used the generalized Ellis-Bronnikov wormhole metric and found that for $n=2$ we have a single barrier shaped effective potential centered at the throat of the wormhole for any value of orbital angular momentum. For $n\neq2$ we have a symmetric double barrier shaped potential when the orbital angular momentum is zero and a single barrier for nonzero angular orbital momentum. Analytical solutions for the Schr\"{o}dinger equation in the generalized Ellis-Bronnikov spacetime could be found only for $n=2$. Such solutions were given in terms of the confluent Heun functions. Finally, by using a delta-barrier approximation we could find the transmission and reflection coefficients for a non-relativistic particle to traverse the generalized Ellis-Bronnikov wormhole.