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Curated by: For the Love of Physics (233 videos)
In this lecture, we develop the Variational Principle in Quantum Mechanics and see how it can be used to estimate the Ground-state energy of a Harmonic Oscillator. 𓏬𓏬𓏬𓏬𓏬QM Lecture Series Playlist𓏬𓏬𓏬𓏬𓏬 https://youtube.com/playlist?list=PLRN3HroZGu2mCtdalEmZAM2nr1xBWAtUn&si=8ejaL8RrSFQGbtzx 𓏬𓏬𓏬𓏬𓏬Advanced QM Lecture Series𓏬𓏬𓏬𓏬𓏬 https://youtube.com/playlist?list=PLRN3HroZGu2m6qv26ZEzBYbAARTOylrP3&si=3myWiJAS63U5jXJo 𓏬𓏬𓏬𓏬𓏬ELEVATE CLASSES𓏬𓏬𓏬𓏬𓏬 Elevate your preparation with Elevate Classes. Find LIVE & Recorded Courses for Physics IITJAM, CSIR-NET, GATE, TIFR, JEST etc on our platform. 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/10wGjkoaOhnF3yMP7O7yaBTXeljfiUYDA/view?usp=drive_link 𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬 Variational Principle is one of the most powerful approximation methods in quantum mechanics. It tells us that if we choose a reasonable trial wavefunction for a quantum system, the energy calculated from that wavefunction can never be lower than the true ground-state energy. By systematically improving the trial wavefunction and adjusting its parameters, we can therefore obtain increasingly accurate estimates of the ground-state energy—even when the Schrödinger equation cannot be solved exactly. Ee develop this idea from first principles and understand what the Variational Principle actually means, why it works, and how to use it in practice. We then apply the Variational Principle to the Quantum Harmonic Oscillator, calculate a variational estimate of its ground-state energy, and compare our result with the exact solution. This lecture is particularly useful for students preparing for CSIR-NET Physical Sciences, GATE Physics, IIT JAM Physics, JEST, TIFR and other postgraduate physics entrance examinations. 00:00 Variational Principle 04:15 Trial Wavefunction 16:57 Harmonic Oscillator - Ground Energy Estimation 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