Summary
Keywords
Full Transcript
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/1pJrGvPudt0AzrePONJ_eDBZsOJyDUgtE?usp=drive_link 𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬 In quantum mechanics, the wave function of a free particle is often described using plane wave solutions. These plane waves represent particles with definite momentum and energy, but they come with certain issues: Non-Normalizability: Plane waves extend infinitely, meaning their total probability density cannot be normalized to one. This conflicts with the probabilistic interpretation of the wave function. Lack of Localization: A plane wave implies the particle is spread out over all space, making it impossible to determine its exact position. To address these issues, the concept of a wave packet is introduced. A wave packet is a combination of multiple plane waves with different momenta. This superposition of waves results in a localized wave function, allowing the particle to be confined to a specific region in space. Wave packets provide a more accurate representation of free particles in quantum mechanics. They allow for a localized position, which aligns with the probabilistic nature of quantum mechanics, and they can spread over time, reflecting the inherent uncertainty in a particle's momentum and position. 00:00 Introduction 01:19 Schrodinger's Equation - Solution 09:25 Constant Probability Density of Plane waves 12:39 Velocity of Plane waves 15:01 Non-Normalizability of Plane waves 17:24 Concept of Wave Packet 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
Continue this lesson in the app
Install CourseHive on Android or iOS to keep learning while you move.
