Macroscopic Quantum Mechanics, Tunnelling, and Classical Gravity

Macroscopic quantum mechanics is an active area of experimental research, which could benefit from understanding the effects of gravitational interactions in tunnelling. The Schr\"{o}dinger-Newton equation is one method for describing Newtonian gravitational interactions in quantum mechanics. While the Schr\"{o}dinger-Newton equation has been thoroughly described for the single-particle case, there are still open questions in the many-body case. Therefore, we investigate semi-classical solutions to the Schr\"{o}dinger-Newton equation for the many-body quantum tunnelling case using a variational-WKB method.