Ehrenfest's Theorem - The Bridge b/w Quantum & Classical Physics (DERIVATION)

What is the connection between Quantum & Classical Physics? Under what circumstances do the Schrodinger Equation give us the Newton's Laws? This is what we discuss in today's lecture - The Ehrenfest Theorem 𓏬𓏬𓏬𓏬𓏬ELEVATE CLASSES𓏬𓏬𓏬𓏬𓏬 Browse LIVE & Recorded Courses for Physics IITJAM, CSIR-NET, GATE, TIFR, JEST etc on our platform ► 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/15Jyk... 𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬 The Ehrenfest theorem relates the average behavior of quantum systems to the classical equations of motion. The theorem states that, on average, the expectation values of quantum mechanical observables follow classical equations of motion. In simpler terms, the Ehrenfest theorem states that the time evolution of the expectation value of momentum is given by the negative of the expectation value of the gradient of the potential. This lecture requires an understanding of the Schrodinger Equation, and the expectation values of position and momentum. While quantum mechanics introduces new concepts and behaviors at the microscopic level, the average behavior of a large number of quantum particles tends to resemble classical mechanics. The Ehrenfest theorem provides a formal expression of this connection, emphasizing the transition from quantum to classical behavior in macroscopic systems. 00:00 Introduction 02:46 The Ehrenfest Theorem 20:54 Connection to Newton's Law 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 ❤️❤️❤️  / dibyajyotidas   Donate/ Paypal 🔥🔥🔥 https://paypal.me/FortheLoveofPhysics JOIN MEMBERSHIP in Youtube 😇😇😇    / @fortheloveofphysics