Quantum Mechanics - Finite Potential Well in Quantum Mechanics (Step by Step Derivation)

In this video, I discuss the Finite Potential Well Problem in ID. I use the Schrodinger Equation to derive the nature of the wavefunction solutions, use boundary conditions to obtain the Transcendental equations, solve them graphically, obtain an expression for number of bound states in a finite well, and show you how to calculate the Energy level of those bound states. 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: https://drive.google.com/file/d/1biLjkz14qogvY6SRvQdZnmEkpq5621aQ/view?usp=sharing 𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬 A finite potential well is a fundamental concept in quantum physics that describes a region where particles, such as electrons, are confined by a potential energy barrier that has a limited height. Unlike an infinite well, where the barriers are insurmountable, a finite well allows for some interaction between the confined region and the surrounding space. In this scenario, particles within the well possess specific, discrete energy levels, much like electrons orbiting an atom. These energy states are determined by the depth and width of the well. Importantly, because the potential barriers are not infinitely high, the particles’ quantum wavefunctions extend slightly beyond the well’s boundaries. This phenomenon, known as quantum tunneling, means there is a probability that particles can exist outside the well, even if their energy is less than the height of the barriers. 00:00 Introduction 03:08 Schrodinger Equation Solutions 17:09 Boundary Conditions 22:53 Transcendental Equations 32:03 Bound State Solutions (Graphical Analysis) 47:05 Energy Calculation (Numeriacal) 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