Coherent states 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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📚 The coherent states of the quantum harmonic oscillator are defined as the eigenstates of the lowering operator. This seemingly simple definition leads to a plethora of properties that make coherent all-important. For example, they are the states that most closely resemble the motion of a classical harmonic oscillator, and in this context they are called quasi-classical states. As another example, they play a key role in the study of quantum optics. In this video, we define coherent states and investigate some of their most basic properties.

0:00 Intro
2:41 Definition of coherent states
4:16 Coherent states in the energy basis
12:04 Time evolution of coherent states
16:19 The raising operator has no eigenstates
21:04 Wrap-up

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⏮️ BACKGROUND
Quantum harmonic oscillator:    • The quantum harmonic oscillator  
Ladder operators:    • Ladder and number operators of the qu...  
Quantum harmonic oscillator eigenvalues:    • Eigenvalues of the quantum harmonic o...  
Eigenvalues and eigenstates:    • Eigenvalues and eigenstates in quantu...  
Representations:    • Representations in quantum mechanics  
Schrödinger equation:    • The Schrödinger equation  

⏭️ WHAT NEXT?
Quasi-classical states:    • Quasi-classical states: does the quan...  
Displacement operator:    • The displacement operator in quantum ...  
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