Uploaded August 2022 | Updated September 2026, 19 minutes ago
An electron (red/yellow wave) interacts with a proton (blue dot) via a nonsingular Coulomb potential, V(r) = -1/(r+ε). The system is confined to a box with perfectly reflecting walls (grey square). The mean position of the electron is shown by a cyan curve.
The time evolution of the electron probability density has been obtained by numerically solving the time-dependent Schrödinger equation.
The following three scenarios have been considered: initially, the electron
(1) has large tangential velocity,
(2) has small tangential velocity,
(3) experiences a free fall.
An electron (red/yellow wave) interacts with a proton (blue dot) via a nonsingular Coulomb potential, V(r) = -1/(r+ε). The system is confined to a box with perfectly reflecting walls (grey square). The mean position of the electron is shown by a cyan curve.
The time evolution of the electron probability density has been obtained by numerically solving the time-dependent Schrödinger equation.
The following three scenarios have been considered: initially, the electron
(1) has large tangential velocity,
(2) has small tangential velocity,
(3) experiences a free fall.
![Quantum Zeno Effect [QBE Ep. 4]](https://i.ytimg.com/vi/lgYDb7gKhKM/mqdefault.jpg "Quantum Zeno Effect [QBE Ep. 4]
Episode 4 of Quantum on the Back of an Envelope [QBE].
🔗 Watch the full series here: https://www.youtube.com/playlist?list=PLIGRVb L3EpDzApE5EnAOYyTAyagvi1W
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.")
![Spontaneous Singularities [QBE Ep. 1]](https://i.ytimg.com/vi/oNhus9iAyys/mqdefault.jpg "Spontaneous Singularities [QBE Ep. 1]
Episode 1 of Quantum on the Back of an Envelope [QBE].
🔗 Watch the full series here: https://www.youtube.com/playlist?list=PLIGRVb L3EpDzApE5EnAOYyTAyagvi1W
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.")
![Do Wave Functions Vanish at Infinity? [QBE Ep. 5]](https://i.ytimg.com/vi/t8x4Kw11c80/mqdefault.jpg "Do Wave Functions Vanish at Infinity? [QBE Ep. 5]
Episode 5 of Quantum on the Back of an Envelope [QBE].
🔗 Watch the full series here: https://www.youtube.com/playlist?list=PLIGRVb L3EpDzApE5EnAOYyTAyagvi1W
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.")
