The displacement operator in quantum mechanics

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

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📚 In this video we learn about the mathematical properties of the displacement operator in the context of the quantum harmonic oscillator. We also learn that the application of the displacement operator on the ground state of the harmonic oscillator generates a coherent state.

0:00 Intro
2:28 Definition
5:54 Mathematical properties
15:36 Coherent states
19:45 Wrap-up

⏮️ BACKGROUND
Quantum harmonic oscillator:    • The quantum harmonic oscillator  
Ladder operators:    • Ladder and number operators of the quantum...  
Coherent states:    • Coherent states in quantum mechanics  

⏭️ WHAT NEXT?
Coherent state wave function || Maths:    • Coherent state wave function || Maths  
Coherent state wave function || Concepts:    • Coherent state wave function || Concepts  

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Director and writer: BM
Producer and designer: MC