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What is Hilbert Space?

Wavefunctions Live in Hilbert Space. What does it mean? What are Hilbert Spaces? In this video, I explore these ideas. 𓏬𓏬𓏬𓏬𓏬Introductory QM Lecture Series Playlist𓏬𓏬𓏬𓏬𓏬    • Quantum Mechanics   𓏬𓏬𓏬𓏬𓏬Advanced QM Lecture Series Playlist𓏬𓏬𓏬𓏬𓏬    • Advanced Quantum Mechanics   𓏬𓏬𓏬𓏬𓏬ELEVATE CLASSES𓏬𓏬𓏬𓏬𓏬 Elevate your preparation with Elevate Classes. Find LIVE & Recorded Courses for Physics IITJAM, CSIR-NET, GATE, TIFR, JEST etc on our platform. New Physics IIT-JAM 2026 Live Batch is starting FEB 15. JOIN NOW 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/drive/folder... 𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬 A Hilbert space is a mathematical space where quantum states are represented as vectors. It is a type of inner product space, meaning we can define lengths (norms) and angles (inner products) between vectors, which helps describe concepts like superposition and probability in quantum mechanics. This linear vector space is also complete, meaning it includes all possible states and their limits, ensuring the mathematics is consistent even for infinitely many quantum states. In this video I describe what Hilbert spaces are, in detail. I talk about Linear Vector spaces - Vector Addition, Scalar Multiplication. I also talk about Inner product, positive norm, completeness and separability. 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