L13.2 The harmonic oscillator: analytic method solution

#harmonicoscillator #analyticmethod #quantummechanicslectures #griffithslectures 0:00 - Introduction to the Schrödinger Equation and Derivatives 0:20 - Deriving the First and Second Derivatives of the Wave Function 1:57 - Simplifying the Differential Equations 3:37 - Working with Exponentials and Simplification 5:09 - Final Form of the Differential Equation 6:11 - Comparing and Simplifying Equations 7:47 - Cancelling Terms and Reaching the Hermite Equation 8:52 - Introduction to the Power Series Method 9:27 - Setting Up the Power Series Solution 10:49 - Deriving the First and Second Derivatives of the Power Series 12:00 - Applying Power Series to Solve the Equation Lecture Notes: https://drive.google.com/file/d/1djSzyt3cAohevKGKvg5VI-cHO9Vvok3r/view?usp=sharing Complete Playlist at: https://www.youtube.com/watch?v=dA40a9Xs3NU&list=PLeWSImvDbpletkUAuNP6DnechsA29wCkN This lecture focuses on solving the Schrödinger equation using the power series method, specifically exploring the derivation of the Hermite equation, which is a crucial part of quantum mechanics. It begins with the calculation of the second derivative of a wave function and then proceeds to derive and simplify the differential equations. The lecture also introduces the power series solution method to solve these equations and demonstrates how to calculate the first and second derivatives of the wave function. The lecture concludes by showing how to apply the power series method to find the solution to the Hermite equation. the harmonic oscillator, analytic method, harmonic oscillator - the series solution, quantum harmonic oscillator, harmonic oscillator quantum mechanics, solution harmonic oscillator, harmonic oscillator with friction, questions on harmonic oscillator, ideal harmonic oscillator with python code, solving harmonic oscillator, introduction to harmonic oscillators, the linear harmonic oscillator, harmonic oscillator potential, 2d harmonic oscillator, simple harmonic oscillator