Coherent state wave function || Concepts

📝 Problems+solutions: - Quantum harmonic oscillator I: https://professorm.learnworlds.com/course/quantum-harmonic-oscillator-i - Quantum harmonic oscillator II: https://professorm.learnworlds.com/course/quantum-harmonic-oscillator-ii 💻 Book a 1:1 session: https://docs.google.com/forms/d/e/1FAIpQLScUL187erItvC7GPnNU2pelsueyVFr94nRq2A5Eq2aVRdGiIQ/viewform?pli=1 📚 Coherent states of the quantum harmonic oscillator are those states that most closely resemble the classical oscillator. In this video we explore this from the perspective of the wave function of coherent states. We find that it has a Gaussian shape, which is consistent with the fact that coherent states are minimum uncertainty states. We also explore the time evolution of the coherent state wave function, revealing the back-and-forth motion that we traditionally associated with harmonic oscillators. 0:00 Intro 4:16 Coherent state wave function 8:06 Minimum uncertainty state 9:40 Displacement operator 11:02 Time evolution 14:31 Wrap-up ⏮️ BACKGROUND Quantum harmonic oscillator: https://youtu.be/OdizRUe84bg Ladder operators: https://youtu.be/Kb9twGd25P0 Quantum harmonic oscillator eigenstates: https://youtu.be/0o-LoJRtxDc Coherent states: https://youtu.be/x0wk98uMyys Quasi-classical states: https://youtu.be/0ef1rLO6DTU Displacement operator: https://youtu.be/ypRTLIo-IIc Minimum uncertainty states: https://youtu.be/cX9JiQ8nEL4 ⏭️ WHAT NEXT? Coherent state wave function || Maths: https://youtu.be/0p9pH85SLIU ~ Director and writer: BM Producer and designer: MC