Hermitian Operator - Properties & Hermitian Conjugate | Explained

What are Hermitian Operators in Quantum Mechanics? In this video I discuss Hermitian Adjoint (or Conjugate) and the various important properties (theorems) of Hermitian Operators. 𓏬𓏬𓏬𓏬𓏬QM Lecture Series Playlist𓏬𓏬𓏬𓏬𓏬    • 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. 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: https://drive.google.com/file/d/1ZLti... 𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬 Hermitian operators represent physical observables (like energy, momentum, spin) in quantum mechanics. The defining feature of a Hermitian operator is that its measured values, or eigenvalues, are always real numbers—reflecting the reality of measurable physical quantities. They have the following key properties: 1. Real eigenvalues (ensuring measurable outcomes are real) 2. Orthogonal eigenstates (distinct outcomes correspond to orthogonal states) 3. Complete eigen-basis (any state can be expressed using their eigenstates) Hermitian operators provide the essential bridge between theory and measurement in quantum mechanics. In this video, I discuss the definition, properties and consequences of Hermitian adjoin (or hermitian conjugate) and Hermitian Operators. 00:00 Hermitian Operators 04:28 Hermitian Adjoint 11:31 Properties of Hermitian Operators 30:28 Is d/dx a Hermitian Operator? 38:36 Is d2/dx2 a Hermitian Operator? 42:00 Skew Hermitian Operator 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