Hydrogen Atom – Full Derivation from Schrodinger Equation (Step by Step) | Quantum Mechanics

QM#44: Full (Step by Step) Derivation of the Solutions of the Hydrogen Atom Problem, using Schrodinger Equation in Quantum Mechanics.

𓏬𓏬𓏬𓏬𓏬QM Lecture Series Playlist𓏬𓏬𓏬𓏬𓏬

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/11gW3Bme3fR4colRKIvu08KsEov7–i9c/view?usp=drive_link

𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬
Complete step-by-step derivation of the Hydrogen Atom using the Schrödinger Equation. In this lecture, we solve the hydrogen atom problem in quantum mechanics from scratch — separating the radial and angular parts, solving the angular equation to obtain spherical harmonics, and solving the radial equation to derive the associated Laguerre polynomials, energy eigenvalues, and wavefunctions. Everything is derived rigorously following Griffiths’ conventions. Essential for CSIR NET, GATE, IIT JAM, JEST, and TIFR preparation.

📌 Topics Covered:
Schrödinger Equation in Spherical Coordinates | Separation of Variables | Angular Equation & Spherical Harmonics | Radial Equation | Associated Laguerre Polynomials | Energy Levels | Hydrogen Atom Wavefunctions | Quantum Numbers (n, l, m)

TIMESTAMPS
Hydrogen Atom 00:00
Schrodinger Equation – Separation of Variables 03:04
Azimuthal Equation – Solutions 15:11
Angular Equation – Legendre Polynomials 32:36
Visualizing Spherical Harmonics 59:39
Radial Equation 01:10:21
Asymptotic Behaviour 1:20:58
Power Series Solution – Recursive Formula 1:44:24
Energy Quantisation – Termination of Series 1:55:53
Ground State Solution 2:17:03
Laguerre Polynomials 2:29:55
Radial Solutions 2:48:15
Final Solutions – Orbitals 2:59:14

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