Boson operators
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The single mode boson operators come in two flavours, the creation operator, and the annihilation operator. They are denoted like the following:
The pair are called the "ladder operators". They arise from consideration of the quantum harmonic oscillator. The commutation relation that they satisfy is


![[\hat{b}, \hat{b}^\dagger] = 1](http://upload.wikimedia.org/wikiversity/en/math/d/5/d/d5d83c00e0cfe3f46fc2a4d27efaca11.png)