L13.1 The harmonic oscillator: analytic method solution

#harmonicoscillator #analyticmethod #quantummechanics #quantummechanicslectures #griffithslectures 0:00 - Introduction to the Harmonic Oscillator and the Schrödinger Equation 0:20 - Defining the Schrödinger Equation for the Harmonic Oscillator 0:40 - Introducing the Dimensionless Variable and Simplification 1:00 - Dimensional Analysis and Deriving the Variable Psi 2:00 - Relating Energy to Wave Number and Momentum 3:00 - Transformation of the Schrödinger Equation 4:00 - Simplification and Converting Terms in the Equation 5:00 - Solving for Psi and Introducing New Variables 6:00 - Simplifying the Equation and Defining Energy Terms 7:00 - Defining Normalized Energy and Relation to Ground State Energy 8:00 - Energy Normalization and Defining K 9:00 - Converting to Simplified Form for Psi 10:00 - Approximate Solution of the Schrödinger Equation 11:00 - Asymptotic Solution and Behavior at Extreme Limits 12:00 - Solution to the Differential Equation and General Form of Psi 13:00 - Conditions on the Wave Function and Discarding Trivial Solutions 14:00 - Final Solution for Psi and Normalization Constant 15:00 - Concluding the Solution to the Harmonic Oscillator 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 In this lecture, the focus is on solving the Schrödinger equation for the harmonic oscillator using an analytic method. The lecture begins by defining a dimensionless variable to simplify the equation and discusses the energy relationship within the system. The conversion of the Schrödinger equation into a simplified form is followed by solving for the wave function, including defining energy terms and solving the resulting differential equation. The solution is found through a normalization constant, and the method of deriving the solution in a compact form is explained. harmonic oscillator, 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