Uploaded June 2025 | Updated September 2026, 2 days ago
📘 Lesson 13 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
Can a particle be in two states at once?
In this lesson, you'll discover the principle of quantum superposition—the idea that a quantum system can exist in a combination of multiple states at the same time. We show how wave functions can be added together to form new, valid quantum states, and prove that these superpositions still satisfy the Schrödinger equation. As a striking example, we construct a "cat state" from two spatially separated coherent states of a harmonic oscillator, illustrating how quantum systems can embody classically contradictory properties—like being on the left and right at once.
📝 Solved exercises for this course are available here: quantphys.com/lessons/qm1
📘 Lesson 13 of 21
▶️ Watch the full lecture series here: youtube.com/playlist?list=PLIGRVb_-L3Eokg9bMKOX6XLyVgxlPb8uv
Can a particle be in two states at once?
In this lesson, you'll discover the principle of quantum superposition—the idea that a quantum system can exist in a combination of multiple states at the same time. We show how wave functions can be added together to form new, valid quantum states, and prove that these superpositions still satisfy the Schrödinger equation. As a striking example, we construct a "cat state" from two spatially separated coherent states of a harmonic oscillator, illustrating how quantum systems can embody classically contradictory properties—like being on the left and right at once.
📝 Solved exercises for this course are available here: quantphys.com/lessons/qm1
![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.")
