Episode 3 of Quantum on the Back of an Envelope. In this episode of Quantum on the Back of an Envelope , we explore quantum fractals through one of the simplest quantum-mechanical systems: the particle in a box. The fractal wave function discussed here is based on the paper: M. V. Berry, Quantum fractals in boxes , J. Phys. A: Math. Gen. 29, 6617 (1996) .

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/x ² 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.

The time-dependent Schrödinger equation is usually expressed in position space, with the wave function depending on position and time. This overview presents an alternative formulation in momentum space, where the wave function depends on momentum and time.