Quantum Mechanics - Probability is a Fluid in QM - Probability Current EXPLAINED

What is Probability Current and it's Continuity Equation in Quantum Mechanics is what I discuss in this video lecture. 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/drive/folders/17HBFIxO-DEu5_BuKCJIs8tr3RoAC2yQS?usp=drive_link 𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬 In quantum mechanics, the concept of probability current density plays a crucial role in understanding the behavior of particles described by wave functions. Essentially, it represents the flow of probability associated with the motion of these particles through space. The probability current density provides insights into the movement of particles in quantum systems. For instance, in one-dimensional space, the probability current density can indicate whether a particle is moving to the right or to the left, depending on the sign of J. In three-dimensional space, the vector nature of the probability current density gives more detailed information about the direction and magnitude of particle motion. Moreover, the probability current density is conserved in quantum mechanics, which means that the total probability flux into a region of space must equal the total probability flux out of that region. This conservation property is analogous to the conservation of mass or charge in classical physics. 00:00 Introduction 03:20 Continuity Equation & Probability Current 20:21 Examples 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