The Heisenberg Uncertainty Princeple

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FlyInDance
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Hey Guys, I've got a question, could you help me?
Can you tell me why the minimum of the Heisenberg Uncertainty Princeple is h bar over two, and how can we say the associate state is the Gauss state.
I hope you can do it more mathematically.
 
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See 3.3 and 3.4.3 in Griffiths.
 

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