Solving the Quantum Harmonic Oscillator using the Algebraic Method (Ladder Operators)

In this video I will solve the Quantum Harmonic Oscillator using the Algebraic Method (Ladder Operators).


My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬

0:00 The Quantum Harmonic Oscillator potential
3:00 Introducing the Operators
20:40 Applying the a+ operator to the wavefunction
28:30 Applying the a- operator to the wavefunction
34:20 Visualizing the Ladder Operators
36:40 Determining the Wave Function of the Ground State
40:20 Determining the Energy of the Ground State
41:40 Determining the Energy levels
42:30 Finding the first excited state
46:10 Final results