Ladder and number operators of the quantum harmonic oscillator

📝 Problems+solutions:
Quantum harmonic oscillator I: https://professorm.learnworlds.com/co...
Quantum harmonic oscillator II: https://professorm.learnworlds.com/co...

📚 Ladder operators allow us to increase or decrease the energy of a quantum harmonic oscillator by a discrete amount, called a quantum of energy. The number operator allows us to count the number of energy quanta in the system. In this video, we derive a long list of properties of ladder and number operators that will prove extremely useful in our study of the quantum harmonic oscillator.

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⏮️ BACKGROUND
Hermitian operators:    • Hermitian operators in quantum mechanics  
Harmonic oscillator:    • The quantum harmonic oscillator  

⏭️ WHAT NEXT?
Eigenvalues of the quantum harmonic oscillator:    • Eigenvalues of the quantum harmonic oscill...  
Eigenstates of the quantum harmonic oscillator:    • Eigenstates of the quantum harmonic oscill...  
Ladder operators in angular momentum:    • Ladder operators in angular momentum  

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Director and writer: BM
Producer and designer: MC