Quantum Harmonic Oscillator - Analytic Method for Eigenvalues and Eigenfunctions

Quantum Harmonic Oscillator - Analytic Method for Eigenvalues and Eigenfunctions

For the Love of Physics via YouTube Direct link

00:00 Introduction

1 of 9

1 of 9

00:00 Introduction

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Quantum Harmonic Oscillator - Analytic Method for Eigenvalues and Eigenfunctions

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  1. 1 00:00 Introduction
  2. 2 05:42 Schrodinger Equation - Variable Substitution
  3. 3 12:42 Asymptotic Behavior - Gaussian Function for large x
  4. 4 18:46 Trial Function for small x
  5. 5 25:35 Power Series Solution
  6. 6 33:20 Recursion Relation & Asymptotic Behavior
  7. 7 46:48 Truncation Condition & Energy Eigenvalues
  8. 8 58:49 Hermite Polynomials
  9. 9 1:19:15 Final Results & Plots

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