Quantum Mechanics - Dirac Delta Potential Well - Bound State | Energy Level & Eigenfunction (Derivation)

What is the Quantum Mechanical Solution of a Particle trapped in a Dirac Delta Potential Well? In this video, I do a detailed discusiion. 𓏬𓏬𓏬𓏬𓏬QM Lecture Series Playlist𓏬𓏬𓏬𓏬𓏬 https://youtube.com/playlist?list=PLRN3HroZGu2mCtdalEmZAM2nr1xBWAtUn&si=8ejaL8RrSFQGbtzx 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: 𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬 A quantum particle in a Dirac delta potential well experiences a unique form of confinement — bound to a single point in space by an infinitely narrow, infinitely deep potential. This intriguing system is a classic example in quantum mechanics, revealing how bound states can arise even in the simplest of potentials, and offering deep insights into wavefunctions, probability densities, and the fundamental nature of quantum confinement. In this Video, I derive the Eigenfunction solutions and Energy Eigenvalue for such a system 00:00 Introduction 01:23 Dirac Delta Function 04:54 Delta Potential Well - Setup 09:36 Bound State Eigenfunction Solution 26:43 Energy of Bound State 42:19 Normalisation 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