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Curated by: For the Love of Physics (233 videos)
What are Ladder Operators? And how do they help create an alternate approach to the quantum Harmonic Oscillator problem? In this video we do a step-by-step study of the algebraic method, or operator formalism of Harmonic oscillator using Ladder Operators. 𓏬𓏬𓏬𓏬𓏬Advanced QM Lecture Series Playlist𓏬𓏬𓏬𓏬𓏬 https://youtube.com/playlist?list=PLRN3HroZGu2m6qv26ZEzBYbAARTOylrP3&si=AV1q0goHoby43SIB 𓏬𓏬𓏬𓏬𓏬ELEVATE CLASSES𓏬𓏬𓏬𓏬𓏬 Elevate your preparation with Elevate Classes. Find LIVE & Recorded Courses for Physics IITJAM, CSIR-NET, GATE, TIFR, JEST etc on our platform. Use Coupon LOVEPHYSICS to get a 5% OFF in any course. Website ► https://www.elevateclasses.in/ Android ► https://bit.ly/3zU71ur iOS ► https://apple.co/3ZPRWVJ (use ORG code - AHGXS) 𓏬𓏬𓏬𓏬𓏬LEC NOTES - GDRIVE𓏬𓏬𓏬𓏬𓏬 Find the PDF Scanned copy of my NOTES for this lecture here: https://drive.google.com/file/d/1Uapw294P7wOCtP-S0pQE5_a5l-MDDTNJ/view?usp=drive_link 𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬 Ladder operators are tools in the quantum harmonic oscillator that let you move between energy levels step by step. One operator raises the system to a higher energy state, while the other lowers it to a lower energy state. Instead of solving the full differential equation, they provide a simpler, systematic way to build all possible energy states. 00:00 Introduction 02:53 Hamiltonian of Harmonic Oscillator 14:29 Commutator of Ladder Operator 15:40 Behaviour of Ladder Operators 29:14 Ladder Operation Proof 41:39 Number Operator & Hamiltonian 46:51 Ground State Solution 54:02 Generator of Higher Eigenstates 59:30 Summary of Ladder Operators 01:04:07 Solved Problem 𓏬𓏬𓏬𓏬𓏬𓏬TELEGRAM𓏬𓏬𓏬𓏬𓏬𓏬 Join my Telegram Channel ► https://t.me/FortheLoveofPhysicsYT 𓏬𓏬𓏬𓏬𓏬SUPPORT CHANNEL𓏬𓏬𓏬𓏬𓏬 Your Financial support provides me an additional incentive to create high quality lecture videos. I am very much thankful for your generosity and kindness Support/ Patreon ❤️❤️❤️https://www.patreon.com/dibyajyotidas Donate/ Paypal 🔥🔥🔥 https://paypal.me/FortheLoveofPhysics JOIN MEMBERSHIP in Youtube 😇😇😇 https://www.youtube.com/channel/UCOfLm6gZGt3vwTMKRg-irhg/join