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Episode 5 of Quantum on the Back of an Envelope. In this episode of Quantum on the Back of an Envelope , In this episode of Quantum on the Back of an Envelope, we ask whether a quantum mechanical wave function really has to vanish at infinity — an assumption often made in introductory textbooks and courses. To explore this, we examine a specific example (taken from "Principles of Advanced Mathematical Physics" by Robert D. Richtmyer) of a wave function that is perfectly continuous, differentiable, and normalizable, yet not only refuses to vanish, but actually becomes unbounded at infinity.

Episode 4 of Quantum on the Back of an Envelope. In this episode of Quantum on the Back of an Envelope , we explore how frequent observations -- more precisely, projective measurements -- can dramatically alter the time evolution of a quantum system, and in some cases even freeze it altogether. This fascinating phenomenon is known as the quantum Zeno effect.

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.

Episode 1 of Quantum on the Back of an Envelope. In this first episode of Quantum on the Back of an Envelope , we explore an unexpected phenomenon in quantum mechanics: how a perfectly smooth wave function, evolving under the Schrödinger equation, can spontaneously develop a singularity over time.