Attractive Potential with No Ground State

Episode 2 of Quantum on the Back of an Envelope.

In this episode of Quantum on the Back of an Envelope, we explore the strange and fascinating -1/x² potential. Despite being attractive and infinitely deep, it has no ground state -- and therefore no discrete energy spectrum. In a certain regime, the system can be so unstable that it could (theoretically) destroy the universe. No equations -- just simple dimensional analysis.